Question

Prove the following trigonometric identities.

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

Answer 1

We need to prove

Here, we will first solve the LHS.

Now, using , we get

Further, multiplying both numerator and denominator by , we get

Now, using the property, we get

So,

= RHS

Hence proved.