## Precalculus: Mathematics for Calculus, 7th Edition

$\frac{1}{2}(\sin 5x+\sin 3x)$
Use the second Product-to-Sum Formula on page 559, $\cos u\sin v=\frac{1}{2}[\sin(u+v)-\sin(u-v)]$. $\cos x\sin 4x$ $=\frac{1}{2}[\sin(x+4x)-\sin(x-4x)]$ $=\frac{1}{2}[\sin(5x)-\sin(-3x)]$ $=\frac{1}{2}(\sin 5x+\sin 3x)$