1/sin2A+cos4A/sin4A=cotA-cosec4A
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Answer:
lhs = 1/Sin2A+Cos4A/Sin4A
= 2cos2A/(2cos2A.sin2A) + cos4A/sin4A
= 2cos2A/sin4A + cos4A/sin4A
= (2cos2A + 2cos^2(2A) - 1)/sin4A
= 2cos2A(1+cos2A)/sin4A - 1/sin4A
= 2cos2A(1+2cos^2(A) - 1)/(2cos2A.sin2A) - 1/sin4A
= 2cos^2(A)/sin(2A) - 1/sin4A
= 2cos^2A/(2cosA.sinA) - 1/sin4A
= cosA/sinA - 1/sin4A
= cotA - cosec(4A) = rhs
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