# Which identity is being used to get $\sin(wa)\cos(wt)=\sin(w(a+t))+\sin(w(a-t))$?

Which identity is being used to get $\sin(wa)\cos(wt)=\frac{\sin(w(a+t))+\sin(w(a-t))}{2}$?

Couldn't find it among the trigonometric identities.

• Name any trigonometric identities you checked – Hagen von Eitzen Oct 22 '14 at 17:10
• – user42141 Oct 22 '14 at 17:13
• Check the section Product-to-sum and sum-to-product identities there (and correct the error in your post) – Hagen von Eitzen Oct 22 '14 at 17:15
• @HagenvonEitzen Thanks! What error in my post do you mean? – user42141 Oct 22 '14 at 17:39
• @user42141 You are missing a factor of $2$ in your formula (it shows up when you add the basic identities in my answer below). – ir7 Oct 22 '14 at 19:03

Add $$\sin (x+y) = \sin x\cos y + \cos x\sin y$$ and $$\sin (x-y) = \sin x\cos y - \cos x\sin y.$$