How can I remember trig identities?
Trigonometric identities are sometimes tricky, as they are very hard to distinguish one from another. The best way of doing it is obviously by practising, but one thing I always find helpful is to give an example. In the case of cos(a+b), we expand it as cos(a) * cos(b) - sin(a) * sin(b). How can I check that I am sure? Well, if b = 0, then the right hand side term becomes cos(a)*1-sin(a)*0 = cos(a) = cos(a+0). Checked. Is cos(-a-b) = cos(a+b)? Yes, it is. cos(-a)*cos(-b) = cos(a) * cos(b), as cos is an even function and sin(-a)sin(-b) = -sin(a)(-sin(b)) = sin(a)*sin(b), as sin is odd. Hence the identity is unchanged.
So, we have taken to important properties of trigonometric functions which are still available on our guessed identity, thus we strongly believe is true, which it is.
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