The modulated wave equation is like this: (p+m*cos(y))*cos(x), where x is the pulsation of the carrier and y of the modulating wave,
p is the carrier amplitude and m the modulating wave amplitude.
First member of multiplication between brackets represents the amplitude of the modulated resulting wave.
The quantity m/p is the modulation depth.
But due the trigonometric law cosx*cosy = 1/2*[cos(x-y)+cos(x+y)] the first equation become the sum of three waves, carrier wave, lower side band, upper side band, so we can place three generators in series to obtain the same result.