NCERT solution class 10 chapter 8 Introduction to Trigonometry exercise 8.2 mathematics ~ evidya

EXERCISE 8.2

Q 1 (ii & iii), Ex 8.2 - Trigonometry - Chapter 8 - Maths Class 10th - NCERT

Q 1 (iv & v), Ex 8.2 - Trigonometry - Chapter 8 - Maths Class 10th - NCERT

Page No 187:

Question 1:

Evaluate the following
(i) sin60° cos30° + sin30° cos 60°
(ii) 2tan²45° + cos²30° − sin²60°
(iii)

(iv)

(v)

Answer:

(i) sin60° cos30° + sin30° cos 60°

(ii) 2tan²45° + cos²30° − sin²60°

(iii)

(iv)

(v)

Q 2 (i & ii), Ex 8.2 - Trigonometry - Chapter 8 - Maths Class 10th - NCERT

Q 2 (iii & iv), Ex 8.2 - Trigonometry - Chapter 8 - Maths Class 10th - NCERT

Question 2:

Choose the correct option and justify your choice.
(i)

(A). sin60°
(B). cos60°
(C). tan60°
(D). sin30°
(ii)

(A). tan90°
(B). 1
(C). sin45°
(D). 0
(iii) sin2A = 2sinA is true when A =
(A). 0°
(B). 30°
(C). 45°
(D). 60°
(iv)

(A). cos60°
(B). sin60°
(C). tan60°
(D). sin30°

Answer:

(i)

Out of the given alternatives, only

Hence, (A) is correct.
(ii)

Hence, (D) is correct.
(iii)Out of the given alternatives, only A = 0° is correct.
As sin 2A = sin 0° = 0
2 sinA = 2sin 0° = 2(0) = 0
Hence, (A) is correct.
(iv)

Out of the given alternatives, only tan 60°

Hence, (C) is correct.

Q 3, Ex 8.2 - Trigonometry - Chapter 8 - Maths Class 10th - NCERT

Question 3:

and

;
0° < A + B ≤ 90°, A > B find A and B.

Answer:

⇒

⇒ A + B = 60 … (1)

⇒ tan (A − B) = tan30
⇒ A − B = 30 … (2)
On adding both equations, we obtain
2A = 90
⇒ A = 45
From equation (1), we obtain
45 + B = 60
B = 15
Therefore, ∠A = 45° and ∠B = 15°

Q 4, Ex 8.2 - Trigonometry - Chapter 8 - Maths Class 10th - NCERT

Question 4:

State whether the following are true or false. Justify your answer.
(i) sin (A + B) = sin A + sin B
(ii) The value of sinθ increases as θ increases
(iii) The value of cos θ increases as θ increases
(iv) sinθ = cos θ for all values of θ
(v) cot A is not defined for A = 0°

Answer:

(i) sin (A + B) = sin A + sin B
Let A = 30° and B = 60°
sin (A + B) = sin (30° + 60°)
= sin 90°
= 1
sin A + sin B = sin 30° + sin 60°

Clearly, sin (A + B) ≠ sin A + sin B
Hence, the given statement is false.
(ii) The value of sin θ increases as θ increases in the interval of 0° < θ < 90° as
sin 0° = 0

sin 90° = 1
Hence, the given statement is true.
(iii) cos 0° = 1

cos90° = 0
It can be observed that the value of cos θ does not increase in the interval of 0° < θ < 90°.
Hence, the given statement is false.
(iv) sin θ = cos θ for all values of θ.
This is true when θ = 45°
As