Sec^2a-(sin^2a-2sin^4a)/(2cos^4a-cos^2a) =1
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LHS =
sec^2 A-[(sin^2 A-2sin^4 A)/(2cos^4 A-cos^2 A)]
= sec^2 A-[sin^2 A(1-2sin^2 A)/cos^2 A(2cos^2 A-1)]
= sec^2 A-[sin^2 A(cos^A-sin^2 A)/cos^2 A(cos^2 A-sin^2A)]
= sec^2 A-[sin^2 A(cos^A-sin^2 A)/cos^2 A(cos^2 A-sin^2A)]
= sec^2 A-tan^2A
= 1
= RHS
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