Verifying trig identities?

Okay, I've been getting some of these, but I can't seem to verify this identity... any help? Here's the problem

Sin(x+y) + Sin(x-y) = 2sinxcosy

Okay, I've been working on the left side, and distribute, getting:

Sinx + Siny + Sinx - Siny

And, the sinx's add up to the 2sinx that I need for the right side, but the siny's cancel out if I don't change them around. So I changed one of them to 1/cscy... but I can't seem to work with that and the other siny to end up with cosy.

Where did I go wrong, or where do I go with it now?