[tex]\cos^{2} x + \sin^{2} x = 1[/tex]
With this info you can exchange 1 and there you got your answer.
So:
[tex]\frac{\cos^{2}x-1}{\cos x}=-\tan x\sin x \Rightarrow \frac{\cos^{2}x-\left(\cos^{2}x + \sin^2 x\right)}{\cos x}=-\tan x\sin x \Rightarrow[tex]\frac{-\sin^2x}{\cos x}=-\tan x\sin x \Rightarrow \frac{-\sin x \sin x}{\cos x}=-\tan x\sin x \Rightarrow[/tex][/tex]
[tex]\left (-\tan x \right)\cdot \sin x = -\tan x \sin x[/tex]
