Answer
$\frac{\sin 4x}{\sin x}=4\cos x\cos 2x$
Work Step by Step
Start with the left side:
$\frac{\sin 4x}{\sin x}$
Rewrite $\sin 4x$ as $\sin (2*2x)$:
$=\frac{\sin 2*(2x)}{\sin x}$
Use the double-angle formula $\sin 2u=2\sin u \cos u$ where $u=2x$:
$=\frac{2 \sin 2x\cos 2x}{\sin x}$
Use the double-angle formula $\sin 2u=2\sin u \cos u$ where $u=x$:
$=\frac{2(2\sin x\cos x)\cos 2x}{\sin x}$
Simplify:
$=\frac{4\sin x\cos x\cos 2x}{\sin x}$
$=4\cos x\cos 2x$
Since this equals the right side, the identity is proven.
