Question

Show that

$\frac{\sin 8x+\sin 2x}{\cos 2x-\cos 8x}=\cot 3x$

Answer 1

$\frac{\sin 2x+\sin 2x}{\cos 2x-\cos 2x}=\frac{2\sin \left(\frac{8x+2x}{2}\right)\cos \left(\frac{8x+2x}{2}\right)}{2\sin \left(\frac{8x+2x}{2}\right)\sin \left(\frac{8x+2x}{2}\right)}=\frac{2\sin 5x\cos 3x}{2\sin 3x\sin 5x}=\cot 3x$