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# How do you verify ##(1-cos^2x)(1+cos^2x)=2sin^2x-sin^4x##?

Prove ( 1 - cos ^2 x) (1 + cos^2 x) = 2sin^2 x - sin^4 x

Replace ##( 1 - cos^2 x)## by ##sin^2 x## and ##cos^2 x## by ##1 -sin^2 x##, we get: ##(1 - cos ^2 x) (1 + cos^2 x)## = ##sin^2 x ( 1 + 1 - sin^2 x) ##= ##sin^2 x (2 - sin^2 x) = 2sin ^2 x - sin^4 x##