Question

Solve the following equation:
$\cos x-\sqrt{3}\sin x=\cos 3x.$

Answer 1

$\cos x-\cos 3x=\sqrt{3}\sin x$

$2\sin 2x\sin x=\sqrt{3}\sin x$

So, $\sin x=0,x=n\pi .$ and $\sin x=\frac{\sqrt{3}}{2},x=n\pi +{(-1)}^n\frac{\pi }{3}.$