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

Mathematics in ICSE Class 9 is one of the most challenging and trickiest subjects of all. It includes complex topics such as logarithms, expansions, indices and Pythagoras Theorem which are difficult to understand for an average student. TopperLearning provides study materials for ICSE Class 9 Mathematics to make the subject easy and help students to clear all their concepts. Our study materials comprise numerous video lessons, question banks, revision notes and sample papers which help achieve success in the examination.

Read  more
Page / Exercise

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

Loading...

Key Features of Study Materials for ICSE Class 9 Maths:

  • Include video lessons, question bank and solved sample papers
  • Designed according to the latest ICSE syllabus
  • Developed by subject experts
  • Content revised from time to time
  • Helpful when doing quick revision
  • Guidance when doing homework
  • Understand concepts easily
  • Significantly improve your Mathematics score