Prove the following trigonometric identities:
cosec2θ−sec2θ≡cot2θ−tan2θ\text{cosec}^2\theta - \sec^2\theta \equiv \cot^2\theta - \tan^2\thetacosec2θ−sec2θ≡cot2θ−tan2θ
(cosecθ−sinθ)2≡cot2θ−cos2θ(\text{cosec}\theta - \sin\theta)^2 \equiv \cot^2\theta - \cos^2\theta(cosecθ−sinθ)2≡cot2θ−cos2θ
