Answer
$\sin x\tan(\frac{x}{2})=1-\cos x$
Work Step by Step
Start with the left side:
$\sin x\tan(\frac{x}{2})$
Use the half-angle formula $\tan(\frac{x}{2})=\frac{1-\cos x}{\sin x}$:
$=\sin x*\frac{1-\cos x}{\sin x}$
Simplify:
$=1-\cos x$
Since this equals the right side, the identity has been proven.
