Verify $ \frac {\cot x \cos x}{\cot x + \cos x} = \frac {\cot x - \cos x}{\cot x \cos x} $

Question

Verify

$$ \frac {\cot x \cos x}{\cot x + \cos x} = \frac {\cot x - \cos x}{\cot x \cos x} $$

Answer 1

by cross multiplication we get $$\cos^2(x)(\cot^2(x)+1)=\cot^2(x)$$ from here we get $$\sin^2(x)(\cot^2(x)+1)=1$$ this is true, since we get $$\cos^2(x)+\sin^2(x)=1$$