# Adding two sine waves out of phase

#### Cerkit

Joined Jan 4, 2009
287
Hi.

Why is it that when adding two sine waves of same amplitude but out of phase is it 2 * Amplitude * sin(theta/2)

How do I get to theta/2

Can someone point me to the derivation of this please?

Thanks

#### Alec_t

Joined Sep 17, 2013
11,892
It comes from the trigonometric identity
sin(A) + sin (B) =2* sin((A+B)/2) * cos ((A-B)/2)