Question

Verify the identity Cos^2x-Sin^2x=1-2sin^2x

Answer 1

$Cos^2x-Sin^2x=1-2sin^2x \\ Cos^2x-Sin^2=cos(2x) \\ 1-2sin^2=cos2x \\ cos(2x) =cos2x \\ \\ \\ Cos^2x-Sin^2x=1-2sin^2x \\ \mathrm{cos^2x+sin^2x=1 ~~~\Rightarrow ~~cos^2x=1-sin^2x} } \\ 1-sin^2x-sin^2x=1-2sin^2x \\ 1-2sin^2x=1-2sin^2x$