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

`(1-2\sin^2\theta)/(2\cos^2\theta-1)=(\cos2\theta)/(\cos2\theta)=1`