Question

Prove the following trigonometric identities.

$\frac{{\tan }^3\theta }{1+{\tan }^2\theta }+\frac{{\cot }^3\theta }{1+{\cot }^2\theta }=\sec \theta \mathrm{cosec}\theta -2\sin \theta \cos \theta$

Answer 1

In the given question, we need to prove

Using the property and, we get

Taking the reciprocal of the denominator, we get

Further, using the identity, we get

Hence proved.