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