# NCERT Solutions for Class 10 Maths Chapter 8 - Introduction to Trigonometry

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## Chapter 8 - Introduction to Trigonometry Exercise Ex. 8.1

Solution 1

In ABC by applying Pythagoras theorem
AC2 = AB2 + BC2
= (24)2 + (7)2
= 576 + 49
= 625
AC =  = 25 cm

Solution 2
Solution 3
Solution 4
Solution 5
Solution 6

Since A and B are acute angles, then C is a right angle.

cos A = cos B .... given

AC/AB = BC/AB

AC = BC

B =A           .... angles opposite to equal sides are equal in length.

Solution 7
Solution 8
Solution 9
Solution 10
Solution 11

Solution 1
Solution 2

Solution 3
Solution 4

## Chapter 8 - Introduction to Trigonometry Exercise Ex. 8.3

Solution 1
Solution 2

Solution 3

Given that

tan 2A = cot (A - 18)

cot (90 - 2A) = cot (A -18)
90 - 2A = A - 18
108 = 3A
A = 36

Solution 4

Given that
tan A = cot B
tan A = tan (90 - B)
A = 90 - B
A + B = 90

Solution 5

Given that
Sec 4A = cosec (A - 20)
Cosec (90 - 4A) = cosec (A - 20)
90 - 4A = A - 20
110 = 5A
A = 22

Solution 6
Solution 7

sin 67 + cos 75
= sin (90 - 23) + cos (90 - 15)
= cos 23 + sin 15

## Chapter 8 - Introduction to Trigonometry Exercise Ex. 8.4

Solution 1
We know that
Solution 2
We know that

Solution 3
Solution 4

(i) 9sec2A - 9tan2A
= 9(sec2A - tan2A)
= 9 (1)            (as sec2A - tan2A = 1)
= 9
Hence alternative (B) is correct.

(ii) (1 + tanθ + secθ) (1 + cotθ - cosecθ)

Hence alternative (C) is correct.

(iii) (secA + tanA) (1 - sinA)

(iv)

Solution 5

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