Answer
$\sin 8x=2\sin 4x \cos 4x$
Work Step by Step
Start with the left side, rewrite $8x$ as $2*4x$, and then use the double-angle formula $\sin 2s=2 \sin s \cos s$ with $s=4x$:
$\sin 8x$
$=\sin (2*4x)$
$=2\sin 4x \cos 4x$
Since this equals the right side, the identity is proven.