1. Trig Identity

I need help with proving this trig identity. I tried doing it out but I'm not sure if I'm doing it right since it's getting so expanded. Is there any other way to do it than making the cos4x = cos(2x + 2x) = cos2xcos2x-sin2xsin2x = ...?

Here's the identity:

$\frac{\cos4x + \cos2x}{\sin4x + \sin2x} = \cot3x$

2. Use the identities

$\cos\alpha+\cos\beta=2\cos\frac{\alpha+\beta}{2}\c os\frac{\alpha-\beta}{2}$

$\sin\alpha+\sin\beta=2\sin\frac{\alpha+\beta}{2}\c os\frac{\alpha-\beta}{2}$