Trigonometric Identities

sin(a+b) = sina cosb + cosa sinb
sin(a-b) = sina cosb - cosa sinb
cos(a+b) = cosa cosb - sina sinb
cos(a-b) = cosa cosb + sina sinb

Is there a way to prove these using calculus? (Using derivatives and integrals).

Their form looks a lot like the product rule (xy)' = xy'+x'y. If we take the first one, for example...

int (sina cosb + cosa sinb) = (sina)(cos b)

I'm not sure how to derive the above equation to make it look like sin(a+b).

Why would you prove them using calculus? You can just use basic algebra to do so.

http://en.wikipedia.org/wiki/Proofs_of_t...identities

Oh, pineapple. 3 months of holidays and my brains are fried. Can't help you on this one. There is a way, but I just can't remember it now.

Why would you prove them using calculus? You can just use basic algebra to do so.

Because it drives me nuts that the form looks so much like the product rule.

Someone help me out please?

Your integral is incorrect. You can't integrate wrt a and b at the same time. The trig identities have nothing to do with product rule.