RMS voltage and superposition of the RMS values of two voltage sources, " EX 10 Vidéo 1, 1 "

A load R is supplied by a compound voltage source Vs(t) = Vs1(t) + Vs2(t), the first term of which is Vs1(t) = 4cos(t) [V] and the second term is Vs2(t) = 5sin(t) [V].
Determine the average power Pmoy (or active power P) supplied to load R, given that Pmoy=P=Veff²/R.
Note: RMS voltage Veff is only equal to (Vmax)/(2^1/2) if Vs(t) is a single sinusoidal or cosinusoidal function. In this case, Vs(t) is a sum of two functions, so Veff is not equal to (Vmax)/(2^1/2). We need to use the general formula for rms values, by developing and integrating the functions [sin(t)]² and sin(t)*cos(t) to arrive at the rms voltage Veff, in order to calculate Pmoy.
This application exercise will help you understand how harmonic currents, made up of several sinusoidal terms, overheat three-phase motor connection boxes, leading to premature wear and tear, and cause circuit breakers and even subscriber circuit breakers to trip unexpectedly. These phenomena, or rather problems, will be analysed in detail when we look at the effects of harmonic voltages and currents.