Question

Prove the following trigonometric identities.

$\frac{1}{\sec A+\tan A}-\frac{1}{\cos A}=\frac{1}{\cos A}-\frac{1}{\sec A-\tan A}$

Answer 1

In the given question, we need to prove .

Here, we will first solve the L.H.S.

Now, using, we get

On further solving, we get

Similarly we solve the R.H.S.

Now, using, we get

On further solving, we get

So, L.H.S = R.H.S

Hence proved.