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

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