Prove: sin^2A+cos^4A=cos^2A+sin^4A
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Lhs= sin^2a+cos^4 a
= sin^2a+(1-sin^2a)^2
= sin^2a+1+sin^4a-2sin^2a
=sin^2a+sin^2a+cos^2a-2sin^2a+sin^4a
=2sin^2a-2sin^2a+sin^4a+cos^2a
=sin^4a+cos^2a= RHS proved
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