Q1: LHS factorises as a difference of two squares. One of those factors is equal to 1 from to a standard identity.

Q2: Replace cosec A with 1/sin A in RHS. Multiply top and bottom of each term by sin A to get

sin A cos A/(1 - sin A) + sin A cos A/(1 + sin A).

Get a common denominator - from a standard identity it reduces to cos^2 A. Combine the fractions etc.