NCERT Solutions Maths Class 10 Exercise 8.2

NCERT Solutions Maths Class 10 Exercise 8.2

Maths Class 10 Exercise 8.2

1. Evaluate:

(i) sin 60° cos 30° + sin 30° cos 60°

(ii) 2 tan2 45° + cos2 30° – sin2 60°

(iii)

(iv)

(v)

Solution: (i) sin 60° cos 30° + sin 30° cos 60°

=

= ¾ + ¼ = 4/4 = 1

(ii) 2 tan2 45° + cos2 30° – sin2 60°

=

= 2 + ¾ - ¾ = 2

(iii)

=

=

=

=

=

(iv)

=

=

=

(v)

=

=

2. Choose the correct option and justify your choice:

(i)

(A) sin 60°            (B) cos 60°            (C) tan 60°            (D) sin 30°

(ii)

(A) tan 90°            (B) 1                       (C) sin 45°              (D) 0

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

(A) 0°                      (B) 30°                   (C) 45°                     (D) 60°

(iv)

(A) cos 60°              (B) sin 60°             (C) tan 60°              (D) sin 30°

Solution: (i) (A)

=

= √3/2 = sin 60°

(ii) (D)

= (1 – 1)/(1 + 1)

= 0/2 = 0

(iii) (A) If A = 0, then

Sin 2A = sin 0° = 0 and 2 sin A = 2 sin 0°

= 2 × 0 = 0

Sin 2A = 2 sin A when A = 0

(iv) (C)

=

= √3 = tan 60°

3. If tan (A + B) = √3 andfind A and B.

Solution: tan (A + B) = √3

tan (A + B) = tan 60°

A + B = 60°                      ………. (i)

tan (A – B) = 1/√3

tan (A – B) = tan 30°

A – B = 30°                      ………. (ii)

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

2A = 90°

A = 45°

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

45° + B = 60°

B = 15°

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

(i) sin (A + B) = sin A + sin B

(ii) The value of sin Î¸ increases as Î¸ increases.

(iii) The value of cos Î¸ increases as Î¸ increases.

(iv) sin Î¸ = cos Î¸ for all values of Î¸.

(v) cot A is not defined for A = 0°.

Solution: (i) False, because for A = 60° and B = 30°,

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

And sin A + sin B = sin 60° + sin 30° = √3/2 + ½ = (√3 + 1)/2

Therefore, sin (A + B) ≠ sin A + sin B

(ii) True, because

It is clear, the value of sin Î¸ increases as Î¸ increases.

(iii) False, because

It is clear, the value of cos Î¸ decreases as Î¸ increases.

(iv) False, since it is only true for Î¸ = 45°.

sin 45° = 1/√2 = cos 45°

(v) True, because tan 0° = 0 and cot 0° = 1/tan 0°

= 1/0 i.e. undefined.