Trigonometric Ratios Of Standard Angles Class-9 Concise ICSE Maths

Trigonometric Ratios Of Standard Angles Class-9 Concise Selina ICSE Mathematics Solutions Chapter-23 . We provide step by step Solutions of Exercise / lesson-23 Trigonometric Ratios Of Standard Angles for ICSE Class-9 Concise Selina Mathematics by R K Bansal.

Our Solutions contain all type Questions with Exe-23 A and Exe-23 B,  Exe-23 C  to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-9 Mathematics .

Trigonometric Ratios Of Standard Angles Class-9 Concise Selina ICSE Mathematics Solutions Chapter-23

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–: Select Topics :–

Exe-23 A,

Exe-23 B,

Exe-23 C,

 

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Exercise 23(A), Trigonometric Ratios Of Standard Angles Class-9 Concise Selina ICSE Mathematics Solutions 

Question 1

find the value of:

(i) sin 30^o cos 30^o

(ii) tan 30^o tan 60^o

(iii) cos² 60^o + sin² 30^o

(iv) cosec² 60^o – tan² 30^o

(v) sin² 30^o + cos² 30^o + cot² 45^o

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

Answer

Question 2

find the value of :

(i) tan² 30^o + tan² 45^o + tan² 60^o

(ii) …………..

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

Solution 2:

Answer

Prove that:

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

(ii) cos 30^o. cos 60^o – sin 30^o. sin 60^o = 0

(iii) cosec² 45^o – cot² 45^o = 1

(iv) cos² 30^o – sin² 30^o = cos 60^o.

(v) ………………

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

Answer

Answer

Question 6

Prove that:

(i) sin 60^o = 2 sin 30^o cos 30^o.

(ii) 4 (sin⁴ 30^o + cos⁴ 60^o)

-3 (cos² 45^o – sin² 90^o) = 2

Answer

 

Answer

Question 8

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

(ii) sec. Cot = cosec; write true or false.

(iii) For any angle , state the value of :

Sin²  θ+ cos².θ

Answer

Answer

(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 √3 = 1.732, find (correct to two decimal place) the value of each of the following:

(i) sin 60^o (ii)  2/ tan 30

Answer

Question 11

Evaluate:

(i) , ………….when A = 15^o.

(ii)  ;……………… when B = 20^o.

Answer

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Trigonometric Ratios Of Standard Angles Class-9 Concise Selina ICSE Mathematics Solutions  Exercise 23(B)

Question 1

Given A = 60^o and B = 30^o, 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) = …………..

Answer

Question 2

If A =30^o, then prove that:

(i) sin 2A = 2sin A cos A = …………..

(ii) cos 2A = cos²A – sin²A

= ……………….

(iii) 2 cos² A – 1 = 1 – 2 sin²A

(iv) sin 3A = 3 sin A – 4 sin³A.

Answer

Answer

Question 4

If A = 30^o; show that:

(i) sin 3 A

= 4 sin A sin (60^o – A) sin (60^o + A)

(ii) (sin A – cos A)² = 1 – sin 2A

(iii) cos 2A = cos⁴ A – sin⁴ A

(iv) ………….

(v) ……………= 2 cos A.

(vi) 4 cos A cos (60^o – A). cos (60^o + A)

= cos 3A

(vii) …………… =3

Answer

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Trigonometric Ratios Of Standard Angles Exe-23 (C) for Class-9 Concise Selina ICSE Mathematics Solutions 

Question 1

Solve the following equations for A, if :

(i) 2 sin A = 1 (ii) 2 cos 2 A = 1

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

(v) √3 tan A = 1 (vi) tan 3 A = 1

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

Answer

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

Answer

 

Answer

Question 4

If 4 cos² x^o – 1 = 0 and 0  x^o  90^o, find:

(i) x^o (ii) sin² x^o + cos² x^o

(iii) ……………

Answer

Question 5

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

Answer

Question 6

If sin 3A = 1 and 0  A  90^o, find:

(i) sin A (ii) cos 2A

(iii) tan²A – 1/cos² A

Answer

Question 7

If 2 cos 2A = √3 and A is acute, find:

(i) A (ii) sin 3A

(iii) sin² (75^o – A) + cos² (45^o +A)

Answer

Question 8

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

(ii) If 3 tan A – 5 cos B= √3 and B = 90^o, find the value of A.

Answer

Question 9

From the given figure, find:

(i) cos x^o(ii) x^o

(iii) ……………..

(iv) Use tan x^o, to find the value of y.

Answer

Question 10

Use the given figure to find:

(i) tan ^o (ii) ^o (iii) sin^2o – cos^2o

(iv) Use sin ^o to find the value of x.

Answer

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

Answer

Question 12

Solve for x:

(i) 2 cos 3x – 1 = 0 (ii) cos  = 0

(iii) sin (x + 10^o) = 1/2 (iv) cos (2x – 30^o) = 0

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

(vii) 3 tan² (2x – 20^o) = 1

(viii) cos ………….. =√3/2

(ix) sin² x + sin² 30^o = 1

(x) cos² 30^o + cos² x = 1

(xi) cos² 30^o + sin² 2x = 1

(xii) sin² 60^o + cos² (3x- 9^o) = 1

Answer

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

Answer

Question 14

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

(i) sin x^o (ii) x^o (iii) tan x^o

(iv) use cos x^o to find the value of y.

Answer 

Question 15

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

Answer 15:

— End of Trigonometric Ratios Of Standard Angles Class-9 Concise Selina Solutions :–

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