Question

State whether the following 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°

NCERT Class X
Mathematics - Mathematics

Chapter _INTRODUCTION TO
TRIGONOMETRY

Answer 1

(i) sin (A + B) = sin A + sin B.
It is false. 
sin (A + B) = sin A cos B + sin B cos A

(ii) The value of sin θ increases as θ increases.
It is false. It is a periodic function with period 2π. It increases from 0 to π/2, then decreases till 3π/2 and then increases till 2π.

(iii) The value of cos θ increases as θ increases.
It is false. It is a periodic function with period 2π. decreases from 0 to π and then increases till 2π.

(iv) sin θ = cos θ for all values of θ.
It is false. The instances when it is true is θ = (nπ + π/4) where n = 0,1,2,3...

(v) cot A is not defined for A = 0°
It is true. We take cot 0 to be ∞ which is not defined.