## Precalculus: Mathematics for Calculus, 7th Edition

$\sin 8x=2\sin 4x \cos 4x$
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.