Answer
$2\sin 5x\sin x$
Work Step by Step
Use the second Sum-to-Product Formula, $\cos x-\cos y=-2\sin\frac{x+y}{2}\sin\frac{x-y}{2}$.
$\cos 4x-\cos 6x$
$=-2\sin\frac{4x+6x}{2}\sin\frac{4x-6x}{2}$
$=-2\sin\frac{10x}{2}\sin\frac{-2x}{2}$
$=-2\sin 5x \sin(-x)$
$=2\sin 5x\sin x$
