How do you verify the identity: cos^2x-sin^2x=1-2sin^2x?

From the basic definitions of ##sin## and ##cos## and
##cos^2(x)+sin^2(x) = 1##
or
##cos^2(x) = 1 -sin^2(x)##
So
##cos^2(x) – sin^2(x)##
##= (1-sin^2(x))-sin^2(x)##
##= 1-2sin^2(x)##