Question

State true or false.

$\frac{\sin x+\sin 2x}{1+\cos x+\cos 2x}=\tan x$

• A. True
• B. False

Answer 1

The correct option is A True

$\frac{\sin x+\sin 2x}{1+\cos x+\cos 2x}=\frac{\sin x+2\sin x\cos x}{(1+\cos 2x)+\cos x}$

$=\frac{\sin x(1+2\cos x)}{2{\cos }^{2}x+\cos x}$

$=\frac{\sin x(1+2\cos x)}{\cos x(1+2\cos x)}$

$=\frac{\sin x}{\cos x}$

$=\tan x$

So the given relation is $\text{True}$