Specific or Universal methods for proving trig identities So this might seem like an elementary question to everyone here, but does anyone have any direction or method to follow when proving trig identities? For example, when proving LHS = RHS, sometimes the solution can be solved in a way that is algebraically simple but might not seem so at first site. Sometimes, I just end up in an infinite realm of futile expansion and end up back at spot 1. There has to be a universal method, but it seems like one of those things that is just unwritten. I've gone through 4 textbooks, and none of them offer any advice with this respect.
 A: Perhaps one unwritten "universal strategy" is acquiring experience with many such identities. That means, solving lots of identities: doing all assigned homework, and it can only help you to learn if you approach even unassigned problems as challenges to "play around" with. With experience, you develop intuition after time. Intuition isn't something only some lucky folks are born with. It's a gift whose price is hard work, trial-and-error, persistence, and experience.
The more you work with identities, the more you will encounter the some of the most useful "base identities" that you will be able to apply in more complicated identities, again and again. The more you encounter these basis identities, the better you absorb them and understand them for future use. They will start to "stick with you."
But as you develop experience, there is usually a fair degree of trial and error involved; don't let that stop you. Even ending up nowhere is a learning experience (if for no other reason that learning what doesn't necessarily work). 
Problem-solving, of any kind, if the goal is understanding and remembering what you are doing, is rarely a matter of memorizing algorithms or finding one "universal method" to rehearse and apply to all problems you encounter. That kind of "learning" will soon be lost. The more you think about you're doing, and why it works (or doesn't work), the better you'll be able to "grow" the kind of understanding that will "stick with you" and the better you'll develop that lovely intuition that you've worked hard to attain.
