## Precalculus: Mathematics for Calculus, 7th Edition

$2\sin 4x\cos x$
Use the first Sum-to-Product Formula, $\sin x+\sin y=2\sin\frac{x+y}{2}\cos\frac{x-y}{2}$. $\sin 5x+\sin 3x$ $=2\sin\frac{5x+3x}{2}\cos\frac{5x-3x}{2}$ $=2\sin\frac{8x}{2}\cos\frac{2x}{2}$ $=2\sin 4x\cos x$