Answer
$\tan x=\frac{\sin 2x}{1+\cos 2x}$
Work Step by Step
Start from the right side:
$\frac{\sin 2x}{1+\cos 2x}$
Use the double-angle formulas $\sin 2x=2\sin x\cos x$ and $\cos 2x=2\cos^2x-1$:
$=\frac{2\sin x\cos x}{1+2\cos^2x-1}$
Simplify:
$=\frac{2\sin x\cos x}{2\cos^2x}$
$=\frac{\sin x}{\cos x}$
$=\tan x$
Since this equals the left side, the identity has been proven.
