Prove the identity $\cos(2x)\csc^{2}(x)=2\cos(2x)$

Question

Could you help me to prove this identity $\cos(2x)\csc^{2}(x)=2\cos(2x)$

I can only get $$\frac{\cos^2(x)-\sin^2(x)}{\sin^2(x)}=2(\cos^2(x)-\sin^2(x))$$

How do I proceed from there?

Answer 1

The identity $\cos(2x)\csc^2x = 2\cos(2x)$ is false. If $x = 0$, the left-hand side is undefined, but the right-hand side is equal to $2$.