Answer
$-2\cos\frac{7x}{2}\sin\frac{3x}{2}$
Work Step by Step
Use the Sum-to-Product formula $\sin x-\sin y=2\cos\frac{x+y}{2}\sin\frac{x-y}{2}$.
$\sin 2x-\sin 5x$
$=2\cos\frac{2x+5x}{2}\sin\frac{2x-5x}{2}$
$=2\cos\frac{7x}{2}\sin\frac{-3x}{2}$
$=2\cos\frac{7x}{2}*(-\sin\frac{3x}{2})$
$=-2\cos\frac{7x}{2}\sin\frac{3x}{2}$
