Question

Prove the following trigonometric identities.

$\left(\frac{1}{{\sec }^2\theta -{\cos }^2\theta }+\frac{1}{{\mathrm{cosec}}^2\theta -{\sin }^2\theta }\right){\sin }^2\theta {\cos }^2\theta =\frac{1-{\sin }^2\theta {\cos }^2\theta }{2+{\sin }^2\theta {\cos }^2\theta }$

Answer 1

In the given question, we need to prove

Now, using and in L.H.S, we get

Further using the identity, we get

Further using the identity , we get

Now, from the identity, we get

So,

Hence proved.