RD SHARMA Solutions for Class 12-science Maths Chapter 4 - Inverse Trigonometric Functions

Chapter 4 - Inverse Trigonometric Functions Exercise MCQ

Question 36

If Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions then

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Solution 36

Given: Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions  (i)

We know that Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

As we know that Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Comparing the above inequality with (i), we get

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 37

The value of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions is

a. 0.48

b. 0.96

c. 1.2

d. sin 1.2

Solution 37

Let Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

We know that, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 38

The value of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions is

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Solution 38

Let Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

We know that, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 39

If Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions for some x R, then the value of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions is

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Solution 39

Given: Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

We know that Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 40

One branch of cos-1 other than the principal value branch corresponds to

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Solution 40

One branch of cos-1 other than the principal value branch corresponds to Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions.

Question 41

The principal value branch of sec-1 is

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Solution 41

The principal value branch of sec-1is Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions.

Question 42

Which of the following corresponds to the principal value branch of tan-1?

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Solution 42

The principal value branch of tan-1is Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions.

Question 43

Which of the following corresponds to the principal value branch of cosec-1?

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Solution 43

The principal value branch of cosec-1is Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions.

Question 44

The value of the expression Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions is

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Solution 44

Let Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

We know that Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 45

If 3tan-1x + cot-1x = π, then x equals  

a. 0

b. 1

c. -1

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Solution 45

Given: 3tan-1x + cot-1x = π

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 46

The value of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions is

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Solution 46

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Hence, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 47

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions is valid for what value of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

d. all real values of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 47

We know that,

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions when xy < 1

Therefore, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions is valid when Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Hence, the given expression is valid for Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 48

The value of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions is

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Solution 48

We know that,

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions, which is the principal value branch of tan-1x

Now, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

As Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

a. sin 2α

b. sin α

c. cos 2α

d. cos α

Solution 1

Correct option: (a)

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

b.  Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3

2 tan-1 {cosec(tan-1x) - tan (cot-1x)} is equal to

 

a. cot-1x

b. cot-1Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

c. tan-1x

d. None of these

Solution 3

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

a. sin2α

b. cos2α

c. tan2α

d. cot2α

Solution 4

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 5

The positive integral solution of the equation Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

a. x = 1, y = 2

b. x = 2, y = 1

c. x = 3, y = 2

d. x = -2, y = -1

Solution 5

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

d. None of these

Solution 6

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

a. x

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

d. None of these

Solution 7

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

Question 8

The number of solutions of the equation  

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

 

a. 2

b. 3

c. 1

d. None of these

Solution 8

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

a. 4α = 3β

b. 3α = 4 β

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

d. None of these

Solution 9

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 10

The number of real solutions of the equation Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

 

a. 0

b. 1

c. 2

d. Infinite

Solution 10

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 11

If x < 0, y < 0 such that xy = 1, then tan-1x + tan-1y equals

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

c. - π

d. None of these

Solution 11

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

c. Tan θ

d. Cot θ

Solution 12

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

a. 36

b. 36 - 36 cos θ

c. 18 - 18 cos θ

d. 18 + 18 cos θ

Solution 13

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 14

Correct option: (a) 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 15

Let f(x) = ecos-1{sin(x+π/3)}. Then, f(8π/9) =

 

a. e5π/18

b. e13π/18

c. e-2π/18

d. None of these

Solution 15

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

a. 0

b. 1/2

c. -1

d. none of these

Solution 16

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

 

a. 36

b. -36 sin2θ

c. 36 sin2θ

d. 36cos2θ

Solution 17

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 18

If tan-13 + tan-1x= tan-18, then x =

 

a. 5

b. 1/5

c. 5/14

d. 14/5

Solution 18

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 19

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

d. 0

Solution 20

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 21

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

Question 22

If θ = sin-1 {sin (-600°)}, then one of the possible values of θ is

 

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 22

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 23

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 24

If 4 cos-1x + sin-1 x = π, then the value of x is

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 24

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

a. 0

b. -2

c. 1

d. 2

Solution 25

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 26

If cos -1 x > sin-1x, then

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

d. X > 0

Solution 26

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 27

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 28

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

a. 7

b. 6

c. 5

d. None of these

Solution 29

Correct option:(a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 30

If tan-1(cotθ) = 2θ, then θ =

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

d. none of these

Solution 30

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

 

a. 0

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

c. a

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 31

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 32

The value of sin (2(tan-10.75)) is equal to

 

a. 0.75

b. 1.5

c. 0.96

d. Sin-11.5

Solution 32

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

a. 4tan-1x

b. 0

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

d. π

 

Solution 33

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 34

The domain of cos-1(x2 - 4) is

 

a. [3, 5]

b. [-1, 1]

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 34

Correct option: (c) 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

a. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

b. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

c. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

d. Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 35

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Chapter 4 - Inverse Trigonometric Functions Exercise Ex. 4.1

Question 1(i)

Find the value of each of the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(ii)

Find the value of each of the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(iii)

Find the value of each of the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(iv)

Find the value of each of the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(v)

Find the value of each of the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(v)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(vi)

Find the value of each of the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(vi)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(i)

Find the value of each of the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(ii)

Find the value of each of the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(i)

Find the domain of each of the following functions:

 

F(x) = sin-1x2

Solution 3(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(ii)

Find the domain of each of the following functions:

 

 

F(x) = sin-1x + sin x

Solution 3(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(iii)

Find the domain of each of the following functions:

 

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(iv)

Find the domain of each of the following functions:

 

f(x) = sin-1x + sin-12x

Solution 3(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 4

If sin-1x + sin-1y + sin-1z + sin-1t = 2π, then find the value x2 + y2 + z2 + t2.

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Chapter 4 - Inverse Trigonometric Functions Exercise Ex. 4.2

Question 1

Find the domain of definition of f(x) = cos-1 (x2 - 4).

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2

Find the domain of f(x) = 2cos-12x + sin-1 x.

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3

Find the domain of f(x) = cos-1x + cos x.

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 4(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 4(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 4(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 4(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 4(iii)

Find the principal value of each of the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 4(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 4(iv)

Find the principal value of each of the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 4(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 5(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 5(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 5(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 5(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 5(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 5(iii)

?Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 5(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 5(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Chapter 4 - Inverse Trigonometric Functions Exercise Ex. 4.3

Question 1(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(ii)

Find the principal value of each of the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(iii)

Find the principal value of each of the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(iv)

Find the principal value of each of the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(ii)

For the principal values, evaluate each of the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(ii)

Evaluate each of the following:

 

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(iii)

Evaluate each of the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Chapter 4 - Inverse Trigonometric Functions Exercise Ex. 4.4

Question 1(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(iii)

Find the principal value of each of the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(iv)

Find the principal value of each of the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(ii)

Find the principal value of each of the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(i)

Find the domain of

 

sec-1 (3x - 1)

Solution 3(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(ii)

Find the domain of

 

sec-1 x - tan-1x

Solution 3(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Chapter 4 - Inverse Trigonometric Functions Exercise Ex. 4VSAQ

Question 28

Write the value of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Hence, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 39

Write the principal value of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions.

Solution 39

Let Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 46

Write the value of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 46

We know that,

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Hence, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 47

Write the value of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 47

Let Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

The range of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions is R - (-1, 1).

So, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions does not belong to this range.

Thus, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions is undefined.

Hence, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 48

Write the value of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Solution 48

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Hence, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 49

Write the value of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 49

Using the property that, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions when Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions we have

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 50

Write the value of the expression Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 50

We know that Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions when Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

As Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions we have

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 51

Write the principal value of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 51

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Hence, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 52

The set of values of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 52

Let Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Now, range of cosec x is R - (-1, 1)

As Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions does not belong to this range, so cosec x also does not belong to this range.

Thus, the value of x will be undefined.

Hence, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 53

Write the value of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions for x < 0 in terms of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 53

For x < 0,

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Hence, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 54

Write the value of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions for all Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions in terms of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 54

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions for all Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 55

Write the value of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Solution 55

We know that, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 56

If Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions find the value of x.

Solution 56

Given: Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 57

Find the value of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 57

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Hence, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 58

If Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions find the value of x.

Solution 58

Given: Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Hence, the value of x is Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 59

Find the value of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 59

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Hence, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 60

Find the value of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 60

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Hence, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 61

Find the value of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 61

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

As Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Hence, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 62

Find the value of Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 62

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

As Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Hence, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 63

Two angles of a triangle are Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions The third angle of the triangle is

Solution 63

Let Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Now, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Let Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions be the third angle.

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Hence, the third angle is Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1

Write the value of sin-1 Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 24

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 25

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 27

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions
Question 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 30

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 31

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 32

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 35

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 36

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 37

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 37

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 38

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 38

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 40

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 40

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 41

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 41

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 42

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 42

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 43

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 43

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 44

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 44

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 45

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 45

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Chapter 4 - Inverse Trigonometric Functions Exercise Ex. 4.10

Question 10

Solve Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 10

Given: Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Hence, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 1(i)

Evaluate:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(ii)

Evaluate:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(iii)

Evaluate:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(iv)

Evaluate:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(v)

Evaluate:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(v)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2

[ ∏/2 - sin-1 x ] + [ ∏/2 - sin-1y ] = ∏/4

 

sin-1x + sin-1y = ∏ - ∏/4

 

sin-1x + sin-1y = 3∏/4

 

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3

 Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

On adding both the equation

 

Π/2 + sin-1y - cos-1y = Π/2

 

[ Π/2- cos-1y ] - cos-1y = 0

 

cos-1y = Π/4

 

y = 1/2

 

on putting y=1/2 in 2nd equation

 

cos-1x - Π/4 = Π/6

 

cos-1x = Π/4 + Π/6

 

x = cos(Π/4 + Π/6)

 

x = cos(Π/4)cos(Π/6)-sin(Π/4)sin(Π/6)

 

x = (3-1)/22

 

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 4

cot(z) = 0 means z = Π/2, 3Π/2, 5Π/2 ………..

 

cos-1(3/5) + sin-1x = nΠ + Π/2

 

sin-1x = nΠ + Π/2 - cos-1(3/5)

 

sin-1x = nΠ + sin-1(3/5)

 

x = sin(nΠ + sin-1(3/5)) = (-1)n sin (sin-1(3/5))

 

x = (-1)n 3/5

 

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 5

[ Π/2 - cos-1x ]2 + (cos-1x)2 =17Π2/36

 

Π2/4 - Πcos-1x + 2(cos-1x)2 =17Π2/36

 

Let, cos-1x=u

 

2u2 - Πu + Π2/4 - 17Π2/36 = 0

 

2u2 - Πu - 2Π2/9 = 0

 

18u2 - 9Πu -2Π2 = 0

 

On factorizing

 

18u2 - 12Πu + 3Πu -2Π2 = 0

 

6u( 3u -2Π ) + Π( 3u -2Π ) = 0

 

( 3u -2Π )(6u + Π) = 0

 

u = -Π/6, 2Π/3

 

i.e. cos-1x = -Π/6, 2Π/3

 

but range of cos-1x is [0, π]

 

x = cos(Π/2 + Π/6)

 

x = -1/2

 

Question 6

Solve:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 6

sin-1(1/5) + [ Π/2 - sin-1x ] = sin-11

 

sin-1(1/5) + Π/2 - sin-1x = Π/2

 

sin-1(1/5) - sin-1x = 0

 

x = 1/5

 

Question 7

Solve:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 7

Π/2 - cos-1x = Π/6 + cos-1x

 

Π/3 = 2cos-1x

 

cos-1x = Π/6

 

x = √3/2

 

Question 8

Solve:

 

4 sin-1x = Π - cos-1x

Solution 8

4sin-1x+cos-1x=Π

3sin-1x+sin-1x+cos-1x=Π

3sin-1x=Π/2 [sin-1x+cos-1x=Π/2]

sin-1x=Π/6

x = sinΠ/6=0.5

Question 9

Solve:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 9

tan-1x+cot-1x=Π/2 so the above equation reduces to

cot-1x =2Π/3-Π/2 =Π/6

x= cotΠ/6 =√3

Chapter 4 - Inverse Trigonometric Functions Exercise Ex. 4.11

Question 3(x)

Solve the following equations for x:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Solution 3(x)

Given: Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

As Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 3(xi)

Solve the following equations for x:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Solution 3(xi)

Given: Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

As Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

But Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions does not satisfy the given equation.

Therefore, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 1(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(iii)

Prove the following result:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions


Question 3(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions
Question 3(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(iv)

Solve the following equations for x :

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(v)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(v)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions
Question 3(vi)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(vi)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(vii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(vii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(viii)

Solve the following equations for x:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(viii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(ix)

Solve the following equations for x:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(ix)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 4

Sum the following series:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

 

Chapter 4 - Inverse Trigonometric Functions Exercise Ex. 4.12

Question 3(iii)

Solve the following:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Solution 3(iii)

Given: Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(i)

Solve the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(ii)

Solve the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Chapter 4 - Inverse Trigonometric Functions Exercise Ex. 4.13

Question 5

Prove that: Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 5

Let Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Let Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

We know that, sin(x + y) = sinx cosy + cosx siny

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2

Solve the equation:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3

Solve :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 4

Prove that:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Chapter 4 - Inverse Trigonometric Functions Exercise Ex. 4.14

Question 4(iii)

Prove that: Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 4(iii)

Let Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Hence, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 8(v)

Solve the following equation for x:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Solution 8(v)

Given: Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 8(vi)

Solve the following equation for x:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Solution 8(vi)

Given: Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Using the formula Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 1(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(ii)

Evaluate the following

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(iv)

Evaluate the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions
Question 2(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(v)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(v)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(vi)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(vi)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions
Question 2(vii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(vii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(viii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(viii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions
Question 2(ix)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(ix)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(x)

Prove the following result :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(x)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 4(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 4(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 4(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 4(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 7(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 7(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 7(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 7(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 8(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 8(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions
Question 8(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 8(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 8(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 8(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 8(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 8(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Thus, the solution is Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions
Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Chapter 4 - Inverse Trigonometric Functions Exercise Ex. 4.7

Question 1(i)

Find the value of each of the following:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Solution 1(i)

We know that,

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Hence, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(ii)

Evaluate Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(ii)

We know that,

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Hence, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 2(iv)

Evaluate Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(iv)

We know that,

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Hence, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(ii)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(iii)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(iv)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(v)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(v)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(vi)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(vi)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(vii)

Evaluate the following :

 

sin-1(sin 3)

Solution 1(vii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(viii)

Evaluate the following :

 

sin-1 (sin 4)

Solution 1(viii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(ix)

Evaluate the following :

 

sin-1 (sin 12)

Solution 1(ix)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(x)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(x)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(v)

Evaluate the following :

 

cos-1 (cos 3)

Solution 2(v)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(vi)

Evaluate the following :

 

cos-1 (cos 4)

Solution 2(vi)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(vii)

Evaluate the following :

 

cos-1 (cos 5)

Solution 2(vii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(viii)

Evaluate the following :

 

cos-1 (cos 12)

Solution 2(viii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(i)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(ii)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(iv)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(v)

Evaluate the following :

 

tan-1 (tan 1)

Solution 3(v)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(vi)

Evaluate the following :

 

tan-1 (tan 2)

Solution 3(vi)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(vii)

Evaluate the following :

 

tan-1 (tan 4)

Solution 3(vii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(viii)

Evaluate the following :

 

tan-1 (tan 12)

Solution 3(viii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 4(i)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 4(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 4(ii)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 4(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 4(iii)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 4(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 4(iv)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 4(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 4(v)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 4(v)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 4(vi)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 4(vi)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 4(vii)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 4(vii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 4(viii)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 4(viii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 5(i)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 5(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 5(ii)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 5(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 5(iii)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 5(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 5(iv)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 5(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 5(v)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 5(v)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 5(vi)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 5(vi)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 6(i)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 6(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 6(ii)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 6(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 6(iii)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 6(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 6(iv)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 6(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 6(v)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 6(v)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 6(vi)

Evaluate the following :

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 6(vi)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 7(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 7(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 7(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 7(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions
Question 7(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 7(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 7(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 7(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 7(v)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 7(v)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 7(vi)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 7(vi)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 7(vii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 7(vii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 7(viii)

Write each of the following in the simplest form:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 7(viii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 7(ix)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 7(ix)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 7(x)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 7(x)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Chapter 4 - Inverse Trigonometric Functions Exercise Ex. 4.9

Question 1(iii)

Evaluate:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Solution 1(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Hence, Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions 

Question 1(i)

Evaluate:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(ii)

Evaluate:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(i)

Evaluate:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(ii)

Evaluate:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(iii)

Evaluate:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3

Evaluate:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Chapter 4 - Inverse Trigonometric Functions Exercise Ex. 4.5

Question 1(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(ii)

Find the principal value of each of the following:

 

cosec-1 (-2)

Solution 1(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(iv)

Find the principal value of each of the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2

Find the set of values of

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(i)

For the principal value evaluate the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(ii)

For the principal value evaluate the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(iii)

For the principal value evaluate the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(iv)

For the principal value evaluate the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Chapter 4 - Inverse Trigonometric Functions Exercise Ex. 4.6

Question 1(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(ii)

Find the principal value of each of the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(iii)

Find the principal value of each of the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(iv)

Find the principal value of each of the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2

Find the domain of f(x) = cot x + cot-1 x.

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(i)

Evaluate each of the following:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(ii)

Evaluate each of the following:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(iii)

Evaluate each of the following:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3(iv)

Evaluate each of the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Chapter 4 - Inverse Trigonometric Functions Exercise Ex. 4.8

Question 1(i)

Evaluate the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(ii)

Evaluate the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(iii)

Evaluate the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(iv)

Evaluate the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(v)

Evaluate the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(v)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(vi)

Evaluate the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(vi)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(vii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(vii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(viii)

Evaluate the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(viii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 1(ix)

Evaluate the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 1(ix)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(i)

Prove the following result:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(i)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(ii)

Prove the following result:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(ii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(iii)

Evaluate the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(iii)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 2(iv)

Evaluate the following:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 2(iv)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 3

Solve:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Question 4

Solve:

 

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Inverse Trigonometric Functions