Question

Prove that this question:.​

Answer 1

This follows directly from the double angle identity for cosine and the Pythagorean identity:

$\cos2\theta=\cos^2\theta-\sin^2\theta=\begin{cases}2\cos^2\theta-1\\1-2\sin^2\theta\end{cases}$

So we have

$\dfrac{1-2\sin^2\theta}{2\cos^2\theta-1}=\dfrac{\cos2\theta}{\cos2\theta}=1$