Answer:
cotA-cosec4A
Step-by-step explanation:
LHS=1/sin2A + cos4A/sin4A
=1/sin2A +cos4A/2sin2.Acos2A
=1/sin2A (1+cos4A/2cos2A)
=1/sin2A(2cos2A+cos^2A-sin^3A)/2Cos2A
=1/sin2A(2cos2A+cos^2Ac-(1-cos^2A)/2cos2A
=1/sin2A(2cosA(1+cos2A)-1)/2cos2A
=1/sin2A(1+cos2A-1/2cos2A)
=1+cos2A/sin2A-1/sin2A.cos2A
=1+2cos^A-1/2sinA.cosA-1/sin4A
=2cos^A/2sinA.cosA-1/sin4A
=cosA/sinA-1/sin4A
=cotA-cosec4A
=LHS=RHS
