(sec^4)A - (sec^2)=(tan^2)A+(tan^4)A
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LHS = sec^4 A−sec^2 A
=1/(cos^4 A)−1/(cos^2 A)
=(cos^2 A - cos^4 A)/cos^2 A
=(1 - cos^2 A)/cos^4 A
=sin^2 A/cos^4 A
=tan^2 A/cos^2 A
=tan^2 A * sec^2 A
=tan^2 A * (1 + tan^2 A)
=tan^2 A * tan^4 A = RHS
Hence Proved
Identities Used:
(1 - cos^2 A) = sin^2 A
(1 + tan^2 A) = sec^2 A
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