Proving LHS =RHS.
First we consider Left Hand Side (LHS),
=1(sinA+cosA)+1(sinA–cosA)
By taking LCM we get,
=(sinA–cosA+sinA+cosA)(sin2A–cos2A)
=2sinA(1–cos2A–cos2A)
=2sinA(1–2cos2A) .
Then, Right Hand Side =2sinA(1–2cos2A) .
Therefore, LHS = RHS.
Hence proved.