Prove $\cot^2 (2x) + \cos^2 (2x) + \sin^2 (2x) = \csc^2 (2x)$ I'm having massive issues proving this identity:
$$\cot^2 (2x) + \cos^2 (2x) + \sin^2 (2x) = \csc^2 (2x)$$
How is this proven?

Recall the following identities
$$\cos^2{\alpha} + \sin^2{\alpha} = 1$$
$$\cot^2{\beta} + 1 = \csc^2 \beta$$
Hence, $$\cot^2 (2x) + \cos^2 (2x) + \sin^2 (2x) = \underbrace{\cot^2 (2x) + \underbrace{\left(\cos^2 (2x) + \sin^2 (2x) \right)}_{=1}}_{\cot^2(2x)+1 = \csc^2(2x)}$$
