$$\cos 2x+\cos 3x-\sin x-\cos 4x = \sin 6x$$
$\cos 2x+\cos 3x-\sin x-\cos 4x = \sin 6x <=> \cos 3x-\sin x= \sin 6x+\cos4x-\cos2x<=>\cos 3x-\sin x=\sin6x-2\sin3x.sinx<=>\cos 3x-\sin x=2\sin3x.cos3x-2\sin3x.sinx<=>\cos 3x-\sin x=2\sin3x(\cos 3x-\sin x)<=>(\cos 3x-\sin x)(2\sin3x-1)=0$