# How do you prove the identity (sin^3 x + cos^3 x)/(sin x +cos x) = 1 - sin x cosx?

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