I think the important word you are missing is "suitable". You should have THREE double-angle formulas for cosine.
$\displaystyle \cos(2\theta)\;=\;2\cos^{2}(\theta)-1\;=\;1-2\sin^{2}(\theta)\;=\;\cos^{2}(\theta)-\sin^{2}(\theta)$
I believe you will find the last most "suitable" for your conditions. It factors as a difference of squares and should be obvious from there.
It is a quite useful hint. In fact, I think it's rather clever.
$\displaystyle cos(2\theta) = sin(\theta) + cos(\theta)$
Now use the hint: $\displaystyle cos(2\theta) = cos^2(\theta) - sin^2(\theta)$
$\displaystyle cos^2(\theta) - sin^2(\theta) = cos(\theta) + sin(\theta)$
Now factor the left hand side and see what comes of it.
-Dan
Let's put a couple of things on your list of things to learn:
1) Have a little patience with yourself. No sense beating yourself up. Not everything is easy.
2) Just a little LaTeX can go a long way. It takes up WAY less space than scanned images.
Good deal. What else are you working on?