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

${\cos}^{4} x$ - ${\sin}^{4} x$
${\left({\cos}^{2} x\right)}^{2} - {\left({\sin}^{2}\right)}^{2}$
$\left({\cos}^{2} x + {\sin}^{2} x\right) \left({\cos}^{2} x - {\sin}^{2} x\right)$ --applying the formula of ${a}^{2} - {b}^{2}$
 1 × (cos^2x - sin^2x) --- since ${\cos}^{2} x + {\sin}^{2} x$ =1
${\cos}^{2} x - {\sin}^{2} x$