I see how Educated's tip solved the problem, I'm just not sure how I'd have figured that out on my own. It seems arbitrary to multiply everything by until you actually do it.
So if I were to receive this problem on a test, how would I know to do that? Identities are very frustrating for me. It often seems like trying random things until something works.
Just a note: in LaTeX when you use \frac it gives you smaller fractions eg. . This gets really hard to read if you have fractions on fractions. Use \dfrac to give bigger fractions eg.
What I meant was which would give you:
This gives you the answer straight away.
I noticed how close you were to proving the identity and realised that the numerator must be a 1. So if you divided the numerator by sin(x) it will give you 1.
I don't think the missing step below should be too difficult to think of in this sort of topic:
Doing this is more suggestive (I would have thought) than the approach you ended up taking (which pretty much pulls a rabbit out of the hat). You do it as the next step from what you had way back in post #3.