1 - cos 2x/ 1 + cos 2x =

[tex]$\begin{align}\frac{1-\cos2x}{1+\cos2x}&=\frac{1-(2\cos^2a-1)}{1+(2\cos^2a-1)}\\&=\frac{2-2\cos^2}{2\cos^2a}\\&=\frac{\not2(1-\cos^2a)}{\not2\cos^2a}\\&=\frac{1-\cos^2a}{\cos^2a}\\&=\frac{\sin^2a}{\cos^2a}\\&=\boxed{\tan^2a}\end[/tex]