Question

Sin 2x cos 3x-sin 3x cos 2x=1

Answer 1

$\sin 2x \cos 3x-\sin 3x \cos 2x=1;\, \sin(2x-3x)=\sin(-x)=1;$
$\sin x=-1;\, x\in -\frac{\pi}{2}+2\pi k,\,k\in\mathbb{Z}.$