how do you learn trigonometric identities 
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Is there a more efficient method of trig mastery than rote memorization? 

i find myself loosing it in 1st semester calculus, mainly because people are using trigonometric identities i never heard of before. 
Are those usually explained in any way? They're listed in the front of the book, and that's it. We also never did those in Highschool (maybe the people here did, I'm not from here).
I could go ahead and memorize all of those, but I think that's stupid. So where did you learn those or is it just something I'll have to figure out myself?
 A: I started out with just these three trigonometric identities: 
1] Expansion of $\sin(A + B)$ 
2] Expansion of $\cos(A + B)$ 
3] $\sin^2(A) + \cos^2(A) = 1$
Almost every identity I know today can be pretty much easily derived just by using a combination of the three I listed above [1].
Having said that, I used to solve a whole lot of problems with trigonometry and some identities just stuck in my mind (without my conscious need of memorizing). This has helped a lot since it allowed me to identify situations where I could use trigonometry especially in calculus.
So, I would suggest that you need not worry about not knowing a lot of trigonometric identities. On the other hand, do practice a whole bunch of problems wherever you can find them. There is no substitute for practice in mathematics.
[1] Giussepe Negro has given an interesting piece of info regarding these three identities below in the comments section. Do check it out!
A: The Wikipedia page is a good place to start, it gives proofs for most of the basic ones:
Proofs of trigonometric identities
Once you finish that, the page with the list of trigonometric identities has for most of them a proof sketch:
List of trigonometric identities
In general they are worth memorizing - you don't want to have to prove them on the exam.
A: In my opinion, the best option is to derive them.And after using these identities many times, you'll automatically remember, so there is no point in memorizing. Now, deriving trig identities is not a difficult thing. They can be easily done using the euler formula. See this link for example.
http://www.ee.ucla.edu/~panchap/ee102sp/node4.html
