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##