How do you prove cosx - sinx - cos^3x/cosx = sin^2x - tanx?

$\cos x - \sin x - \frac{{\cos}^{3} x}{\cos} x = \frac{{\cos}^{2} x - {\cos}^{3} x - \sin x}{\cos} x =$
$= \frac{\cos x \left(1 - {\cos}^{2} x\right) - \sin x}{\cos} x = {\sin}^{2} x - \sin \frac{x}{\cos} x =$
$= {\sin}^{2} x - \tan x$