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)##

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