Show that $\frac {\sin(3x)}{ \sin x} + \frac {\cos(3x)}{ \cos x} = 4\cos(2x)$ Show that 

$$\frac{\sin(3x)}{\sin x} + \frac{\cos(3x)}{\cos x} = 4\cos(2x).$$


HINT:
$\sin (3x) = 3\sin x - 4 \sin^3 x$
and
$\cos(3x) = 4\cos^3x - 3\cos x$
