Show that $\frac{1-cos2x}{1+cos2x}=tan^2x$
2. From the formulas $\cos 2x = \cos^2 x -\sin^2 x$ and $\sin^2 x + \cos^2 x =1$:
LHS= $\frac{1-\cos 2x}{1+\cos 2x}=\frac{1-\cos^2 x +\sin^2 x}{1+ \cos^2 x -\sin^2 x}=\frac{2\sin^2 x}{2\cos^2 x}=\tan^2 x$=RHS.
Now plug in x=22.5 and solve for $\tan 22.5$.