twin wave phase shift output loss formula

[Quantumplate]

Is there a formula for this anywhere? What I mean by the subject line is when you add 2 waves of the same frequency and amplitude together, but vary the phase. Obviously when in phase the resultant output is doubled, and when 180deg out of phase there is no resultant at all. I can see using circle vectors that at 120 deg phase shift, then the combined output is the same amplitude as each of the two input waves.
Feeling stupid I can't find the formula online!

[Terry Bites]

Lay back and watch this

[Quantumplate]

Great thanks for the link.
So the factor is 2Acos(phi/2) for anyone seeking the nitty gritty.

[CaptDon]

Using the simplified formula posted by Quantumplate can someone post the step by step math for the following two waves, and would this exactly predict the output voltage/power of for instance an R.F. power combiner. Just for reference let's say it is the standard where every port is 50 ohms. So for my inputs, the waves are the same identical pure sinewave frequency but different in phase. Wave one is 1vpp and is the zero degree reference, wave 2 is 2vpp and lags behind wave 1 by 45 degrees. Can you show the step by step math? Thanks!! (I find this interesting because many years ago RCA had an A.M. broadcast band transmitting system where two 25KW transmitters were combined and by the use of phase shift produced a typical A.M. broadcast signal. RCA called it AmpliPhase and I have the brochures. I never worked on one but they were miserably hated by broadcast engineers apparently due to power combiner fires and blowouts. The system could not produce the 110% forward / 99% backward modulation of today's PWM modulated transmitters and the RCA system was often called Ampli-Fuzz by those who worked on it.) Thanks all!!!