I think the important word you are missing is "suitable". You should have THREE double-angle formulas for cosine.
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.
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?