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##