# How do you prove that cos^4x-sin^4x=cos(2x) ?

$f \left(x\right) = {\cos}^{4} x - {\sin}^{4} x = \left({\cos}^{2} x - {\sin}^{2} x\right) \left({\cos}^{2} x + {\sin}^{2} x\right)$
${\cos}^{2} x - {\sin}^{2} x = \cos 2 x$
${\cos}^{2} x + {\sin}^{2} x = 1$