## Precalculus: Mathematics for Calculus, 7th Edition

$\cos^2 5x-\sin^2 5x=\cos 10x$
Start from the right side, write $10x$ as $2*5x$, and use the double-angle formula $\cos 2s=\cos^2 s-\sin^2 s$ with $s=5x$: $\cos 10x$ =$\cos (2*5x)$ $=\cos^2 5x-\sin^2 5x$ Since this equals the left side, the identity is proven.