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Prove that tan^2A + tan^4A = sec^4A – sin^2A.

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Prove that tan2A + tan4A = sec4A – sin2A.

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L.H.S. = tan2A + tan4A 

= tan2A (1 + tan2A) 

= (sec2A – 1) sec2A 

= sec4A – sec2A 

= R.H.S.

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