Question

Prove the following trigonometric identities.

$\left(1+{\tan }^{2}A\right)+\left(1+\frac{1}{{\tan }^{2}A}\right)=\frac{1}{{\sin }^{2}A-{\sin }^{4}A}$

Answer 1

We need to prove .

Using the property , we get

Now, using , we get

Further, using the property, , we get

Hence proved.