# State whether the following are true or false. Justify you answer.

## Question :

(i)  Sin (A + B) = sin A + sin B

(ii)  The value of $$sin \theta$$ increases as $$\theta$$ increases.

(iii)  The value of $$cos \theta$$ increases as $$\theta$$ increases.

(iv)  $$sin \theta$$ = $$cos \theta$$ for all values of $$\theta$$.

(v)  Cot A is not defined for A = 0.

## Solution :

(i)  False. Because

when A = 60 and B = 30. Then,

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

and, sin A + sin B = sin 60 + sin 30  = $$\sqrt{3} + 1\over 2$$

So, sin (A + B) $$\ne$$  sin A + sin B

(ii)  True.

(iii) False

(iv)  False. Because it is true for only $$\theta$$ = 45

(v)  True. Because tan 0 = 0 and cot 0 = $$1\over tan 0$$ = $$1\over 0$$ i.e. not defined.