I'm gonna have a trigonometry/general algebra exam soon. My teacher has told us about some trignometric proofs, and we defined the $\sin$ and $\cos$ int he right way, doing all formal proofs for the formulas $\sin(a\pm b)$ and $\cos(a\pm b)$ for all $a,b\in\mathbb R$.
We'll have to prove some trig identities. That's where I think she'll make us prove some hard exercises. Like, identities that i've never seen.
I've had a sneak peek into a later exam she gave the class, and there was a identity like
$$\sin 2A + \sin 2B + \sin 2C = 4\sin(A)\sin(B)\sin(C)$$
When $A,B,C$ are angles of a triangle.
This is not an identity easy to prove at the middle of an exam, if you never seen it. I don't have enough time to think about it, there are many substitutions I need to make, in order to find the exact one that'll work.
So, how to protect myself against surprises in this test? Does somebody has an idea? Is there a book with these secret identities, that I can try to prove by myself at home?
Can you think of a good exercise or identity that you think will help me in the test?