Prove that $\displaystyle sec^2 \theta + cosec^2 \theta \equiv 4cosec^2 2\theta $
Really not sure about using the compound angle formula. Thanks for any help
$\displaystyle \sec^2\theta+\csc^2\theta=\frac{1}{\cos^2\theta}+\ frac{1}{\sin^2\theta}=\frac{\sin^2\theta+\cos^2\th eta}{\sin^2\theta\cos^2\theta}=$
$\displaystyle =\frac{1}{\sin^2\theta\cos^2\theta}=\frac{4}{4\sin ^2\theta\cos^2\theta}=\frac{4}{\sin^22\theta}=4\cs c^22\theta$