I had a worksheet with quite a few on it and there are two that I just cannot figure out.

The first one is:

$\displaystyle (1-cos x)^2 + 2 cos x = sin^2 x + 2 cos^2 x$

I know that $\displaystyle sin^2 x = 1-cos^2 x$

so I replaced it so that it is

$\displaystyle 1-cos^2 x + 2 cos^2 x$

I'm not sure if that is even in the right direction but I would really appreciate some help.

The second one is:

$\displaystyle \frac {1+\cos x}{1-\cos x}$ = $\displaystyle \frac {(1+\cos x)^2}{\cos^2 x}$

I tried multiplying the left side by the denominater's conjugate and just got

$\displaystyle \frac {(1+\cos x)^2}{1-\cos^2 x}$

from there I don't know where to go or if I'm even on the right track. Thanks for any help!