Question

sin thita +cos thita/sin thita-cos thita+sin thita -cos thita /sin thita + cos thita = 2 sec ^2thita /tan ^2 thita -1

Answer 1

LHS-
=(sin thita + cos thita)²+(sin thita - cos thita)²/sin² thita - cos² thita
=sin²thita+cos² thita + 2.sin thita.cos thita + sin²thita+cos²thita -2.sin thita. cos thita/sin²thita - cos²thita
=2sin²thita+2cos²thita/sin²thita-cos²thita
=2/cos²thita (sin²thita/cos²thita-1)
=2sec²thita/tan²thita-1=RHS