Prove the following trigonometric identities: secA-tanA/secA+tanA = cos^2A/(1+sinA)^2

Question

Prove the following trigonometric identities:

\(\frac{secA-tanA}{secA+tanA}\) =   \(\frac{cos^2A}{(1+sinA)^2}\)

Answer 1

R.H.S : \(\frac{cos^2A}{(1+sinA)^2}\)  = \(\frac{1-sin^2A}{(1+sinA)^2}\) 

=   \(\frac{(1-sinA)(1+sinA)}{(1+sinA)^2}\)      

=    \(\frac{(1-sinA)/cosA}{(1+sinA)/cosA}\)  

Hence Proved.