Answer
See below.
Work Step by Step
$LHS=\frac{(2cos^2\theta-1)^2}{cos^4\theta-sin^4\theta}=\frac{(cos^2\theta-sin^2\theta)^2}{(cos^2\theta+sin^2\theta)(cos^2\theta-sin^2\theta)}=\frac{cos^2\theta-sin^2\theta}{cos^2\theta+sin^2\theta}=cos^2\theta-sin^2\theta=1-2sin^2\theta=RHS$
