I have done this by starting with the equation and ending with the equation .
Putting together my two posts, we get:So we have now done everything we were asked to do. Are there any steps in the working that you don't understand?
As far as your question is concerned, I'm afraid that experience - practice, practice, practice - is the only answer: just like learning to play a musical instrument.
There are just so many trig formulae, it's impossible to give any simple answer as to what to use and when. Since there are so many formulae, I always found it helpful myself - and so I taught my students - to recite the formulae aloud that I was trying to learn. Write them on Post-It stickers, and stick them up in places where you'll see them while you're doing something else - something that doesn't require much brain power (peeling potatoes, painting a fence, listening to your girlfriend, etc, etc) and recite them over and over. (Perhaps I wasn't really serious about the girlfriend bit...)