SELINA Solutions for Class 9 Maths Chapter 23 - Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]

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Chapter 23 - Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] Exercise Ex. 23(A)

Question 1

find the value of:

(i) sin 30o cos 30o

(ii) tan 30o tan 60o

(iii) cos2 60o + sin2 30o

(iv) cosec2 60o - tan2 30o

(v) sin2 30o + cos2 30o + cot2 45o

(vi) cos2 60o + sec2 30o + tan2 45o.

Solution 1

(i)Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(ii)Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iii)Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iv)Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(v)Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(vi)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Question 2

find the value of :

(i) tan2 30o + tan2 45o + tan2 60o

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iii) 3 sin2 30o + 2 tan2 60o - 5 cos2 45o.

Solution 2

(i) Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric RatiosSelina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iii) 3 sin2 30o + 2 tan2 60o - 5 cos2 45o

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

 

Question 3

Prove that:

(i) sin 60o cos 30o + cos 60o. sin 30o = 1

(ii) cos 30o. cos 60o - sin 30o. sin 60o = 0

(iii) cosec2 45o - cot2 45o = 1

(iv) cos2 30o - sin2 30o = cos 60o.

(v) Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(vi) 3 cosec2 60o - 2 cot2 30o + sec2 45o = 0.

Solution 3

(i) LHS=sin 60o cos 30o + cos 60o. sin 30o

=Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios 

(ii) LHS=cos 30o. cos 60o - sin 30o. sin 60o

=Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios=RHS

(iii) LHS= cosec2 45o - cot2 45o

=Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios=RHS

(iv) LHS= cos2 30o - sin2 30o

=Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios=RHS

(v) LHS= Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

=Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios=RHS

(vi) LHS= Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

=Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios=RHS

Question 4

prove that:

(i) sin (2 Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios30o) = Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(ii) cos (2 Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios30o) = Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iii) tan (2 Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios30o) = Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Solution 4

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

 



(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios




(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

 

 

Question 5

ABC is an isosceles right-angled triangle. Assuming of AB = BC = x, find the value of each of the following trigonometric ratios:

(i) sin 45o

(ii) cos 45o

(iii) tan 45o

Solution 5

Given that AB = BC = x

(i)

(ii)

(iii)

Question 6

Prove that:

(i) sin 60o = 2 sin 30o cos 30o.

(ii) 4 (sin4 30o + cos4 60o)

-3 (cos2 45o - sin2 90o) = 2

Solution 6

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Question 7

(i) If sin x = cos x and x is acute, state the value of x.

(ii) If sec A = cosec A and 0o Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric RatiosA Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios90o, state the value of A.

(iii) If tan Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios= cot Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratiosand 0o Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric RatiosSelina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric RatiosSelina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios90o, state the value ofSelina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios.

(iv) If sin x = cos y; write the relation between x and y, if both the angles x and y are acute.

Solution 7

(i)

The angle, x is acute and hence we have, 0 < x

 Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

 

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

 

(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Question 8

(i) If sin x = cos y, then x + y = 45o ; write true of false.

(ii) secSelina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios. Cot Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios= cosecSelina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios; write true or false.

(iii) For any angle Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios, state the value of :

Sin2 Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios+ cos2Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios.

Solution 8

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

if x and y are acute angles,

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric RatiosSelina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratiosis false.

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

 


SecSelina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios. Cot Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios= cosec Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios is true


(iii)


Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Question 9

State for any acute angle whether:

(i) sin increases or decreases as increases:

(ii) cos increases or decreases as increases.

(iii) tan increases or decreases as decreases.

Solution 9

(i)

For acute angles, remember what sine means: opposite over hypotenuse. If we increase the angle, then the opposite side gets larger. That means "opposite/hypotenuse" gets larger or increases.

(ii)

For acute angles, remember what cosine means: base over hypotenuse. If we increase the angle, then the hypotenuse side gets larger. That means "base/hypotenuse" gets smaller or decreases.

(iii)

For acute angles, remember what tangent means: opposite over base. If we decrease the angle, then the opposite side gets smaller. That means "opposite /base" gets decreases.

Question 10

If = 1.732, find (correct to two decimal place) the value of each of the following:

(i) sin 60o (ii)

Solution 10

(i)

(ii)

Question 11

Evaluate:

(i) , when A = 15o.

(ii) ; when B = 20o.

Solution 11

(i) Given that A=

(ii) Given that B=

Chapter 23 - Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] Exercise Ex. 23(B)

Question 1

Given A = 60o and B = 30o, prove that:

(i) sin (A + B) = sin A cos B + cos A sin B

(ii) cos (A + B) = cos A cos B - sin A sin B

(iii) cos (A - B) = cos A cos B + sin A sin B

(iv) tan (A - B) = Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Solution 1

Given A = 60o and B = 30o

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Question 2

If A =30o, then prove that:

(i) sin 2A = 2sin A cos A = Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(ii) cos 2A = cos2A - sin2A

= Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iii) 2 cos2 A - 1 = 1 - 2 sin2A

(iv) sin 3A = 3 sin A - 4 sin3A.

Solution 2

Given A=Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Question 3

If A = B = 45o, show that:

(i) sin (A - B) = sin A cos B - cos A sin B

(ii) cos (A + B) = cos A cos B - sin A sin B

Solution 3

Given that A = B = 45o

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Question 4

If A = 30o; show that:

(i) sin 3 A

= 4 sin A sin (60o - A) sin (60o + A)

(ii) (sin A - cos A)2 = 1 - sin 2A

(iii) cos 2A = cos4 A - sin4 A

(iv) Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(v) Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios= 2 cos A.

(vi) 4 cos A cos (60o - A). cos (60o + A)

= cos 3A

(vii) Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Solution 4

Given that A = 30o

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios 

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(v)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(vi)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(vii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

 

Chapter 23 - Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] Exercise Ex. 23(C)

Question 1

Solve the following equations for A, if :

(i) 2 sin A = 1 (ii) 2 cos 2 A = 1

(iii) sin 3 A = (iv) sec 2 A = 2

(v) tan A = 1 (vi) tan 3 A = 1

(vii) 2 sin 3 A = 1 (viii) cot 2 A = 1

Solution 1

(i)

(ii)

(iii)

(iv)

(V)

(vi)

(vii)

(viii)

Question 2

Calculate the value of A, if :

(i) (sin A - 1) (2 cos A - 1) = 0

(ii) (tan A - 1) (cosec 3A - 1) = 0

(iii) (sec 2A - 1) (cosec 3A - 1) = 0

(iv) cos 3A. (2 sin 2A - 1) = 0

(v) (cosec 2A - 2) (cot 3A - 1) = 0

Solution 2

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(v)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Question 3

If 2 sin xo - 1 = 0 and xo is an acute angle; find :

(i) sin xo (ii) xo (iii) cos xo and tan xo.

Solution 3

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Question 4

If 4 cos2 xo - 1 = 0 and 0 Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios xo Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios 90o, find:

(i) xo (ii) sin2 xo + cos2 xo

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Solution 4

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Question 5

If 4 sin2 - 1= 0 and angle is less than 90o, find the value of and hence the value of cos2 + tan2.

Solution 5

Question 6

If sin 3A = 1 and 0 A 90o, find:

(i) sin A (ii) cos 2A

(iii) tan2A -

Solution 6

(i)

(ii)

(iii)

Question 7

If 2 cos 2A = Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios and A is acute, find:

(i) A (ii) sin 3A

(iii) sin2 (75o - A) + cos2 (45o +A)

Solution 7

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Question 8

(i) If sin x + cos y = 1 and x = 30o, find the value of y.

(ii) If 3 tan A - 5 cos B= Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios and B = 90o, find the value of A.

Solution 8

(i)

Given that x = 30o

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios 

(ii)

Given that B = 90o

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Question 9

From the given figure, find:

(i) cos xo(ii) xo

(iii) Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iv) Use tan xo, to find the value of y.

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Solution 9

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Question 10

Use the given figure to find:

(i) tan Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios(ii) Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios(iii) sin2Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratioso - cos2Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratioso

(iv) Use sin Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratioso to find the value of x.

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Solution 10

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Question 11

Find the magnitude of angle A, if:

(i) 2 sin A cos A - cos A - 2 sin A + 1 = 0

(ii) tan A - 2 cos A tan A + 2 cos A - 1 = 0

(iii) 2 cos2 A - 3 cos A + 1 = 0

(iv) 2 tan 3A cos 3A - tan 3A + 1 = 2 cos 3A

Solution 11

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Question 12

Solve for x:

(i) 2 cos 3x - 1 = 0 (ii) cos Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios = 0

(iii) sin (x + 10o) = Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios (iv) cos (2x - 30o) = 0

(v) 2 cos (3x - 15o) = 1 (vi) tan2 (x - 5o) = 3

(vii) 3 tan2 (2x - 20o) = 1

(viii) cos Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(ix) sin2 x + sin2 30o = 1

(x) cos2 30o + cos2 x = 1

(xi) cos2 30o + sin2 2x = 1

(xii) sin2 60o + cos2 (3x- 9o) = 1

Solution 12

(i)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios 

(iii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(iv)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(v)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(vi)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(vii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(viii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(ix)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(x)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(xi)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

(xii)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Question 13

If 4 cos2 x = 3 and x is an acute angle; find the value of :

(i) x (ii) cos2 x + cot2 x

(iii) cos 3x (iv) sin 2x

Solution 13

(i)

(ii)

(iii)

(iv)

Question 14

In ABC, B = 90o, AB = y units, BC = units, AC = 2 units and angle A = xo, find:

(i) sin xo (ii) xo (iii) tan xo

(iv) use cos xo to find the value of y.

Solution 14

(i)

From

(ii)

(iii)

(iv)

Question 15

If 2 cos (A + B) = 2 sin (A - B) = 1; find the values of A and B.

Solution 15

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios

Adding (1) and (2)

Selina Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles Including Evaluation Of An Expression Involving Trigonometric Ratios