From common trigonometric formulas, I know that
A cos(2πF1t) + A cos(2πF2t) = 2A cos(2π[(F1-F2)/2]t) cos(2π[(F1+F2)/2]t)
where A is the amplitude of both original cosine functions of t, and F1 and F2 are their respective frequencies, the product demonstrates a modulation of the cosine of the average frequency.
Is there a similar product formula if the two original amplitudes are different, i.e..:
A1 cos(2πF1t) + A2 cos(2πF2t) = ?