These NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.2

Question 1.

Evaluate the following:

Solution:

Question 2.

Choose the correct option and justify your choice:

(i) \(\frac{2 \tan 30^{\circ}}{1+\tan ^{2} 30^{\circ}}\) =

(A) sin 600 (B) cos 60°

(C) tan 60° (D) sin 300

(ii) \(\frac{1-\tan ^{2} 45^{\circ}}{1+\tan ^{2} 45^{\circ}}\) =

(A) tan 90° (B) 1

(C) sin 450 (D) O

(iii) sin 2A = 2 sin A is true when A =

(A) 00 (B) 30°

(C) 45° (D) 60°

(iv) \(\frac{2 \tan 30^{\circ}}{1-\tan ^{2} 30^{\circ}}\) =

(A) cos 60° (B) cos 60°

(C) tan 60° (D) sin 300

Solution:

(i) We have given,

(ii) We have given,

(iii) We have given,

Therefore,

sin 2 A = 2 sin A is true only when A = 0°

∴ correct option is (A)

(iv) We have given,

Question 3.

If tan (A + B) = √3 and tan (A – B) = \(\frac { 1 }{ \surd 3 }\); 0° < A + B ≤ 90°; A > B, find A and B.

Solution:

We have given

tan (A + B) = √3

⇒ tan (A + B) = tan 60°

⇒ A + B = 60° … (i)

tan (A – B) = \(\frac { 1 }{ \surd 3 }\)

⇒ tan (A – B) = tan 30°

⇒ A – B = 30° … (ii)

Adding equation (i) and (ii), we get

2A = 90° ⇒ A = 45°

Putting the velue of A in equation (i), we get

45° + B = 60° ⇒ B = 60° – 45° = 15°

Therefore A = 45° and B = 15°

Question 4.

State whether the following statements are true or false. Justify your answer.

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

(ii) The value of sin θ increases as θ increases.

(iii) The value of cos θ increases as θ increases.

(iv) sin θ = cos θ for all values of θ.

(v) cot A is not defined for A = 0°.

Solution:

(i) False, because if A = 60° and B = 30° then

sin (A + B) = sin (60° – 30°)

= sin 90° = 1

sin A + sin B = sin 60° + sin 30°

= \(\frac{\sqrt{3}}{2}+\frac{1}{2}\) = \(\frac{\sqrt{3}+1}{2}\)

∴ sin (A + B) ≠ sin A + sin B, when A = 60° and B = 30°

(ii) True, because the value of sin θ increases as θ increases from θ to 90°, but when θ increases from 90° to 180° then the value of sin 0 decreases.

(iii) False, because the value of cos θ decreases as θ increases from 0 to 90°.

(iv) False, because sin θ = cos θ is true only when θ = 45°. It is not true for all values of θ,

(iv) True, because cot 0° = \(\frac { 1 }{ 0 }\) = not defined.