I see many related posts, but none speaks about the general formula.
Consider the sum of 2 waves of arbitrary frequency, phase and amplitude. Without loss of generality, we can set the first wave as a "reference" to reduce the number of parameters to 3 degrees of freedom. Then the question is what would be its modulated-wave / waves-product form (if it indeed exists):
$$\cos(t)+A\cos(\omega t+\phi)=A_1\big(1+A_2\cos(\omega_1t+\phi_1)\big)\cos(\omega_2 t+\phi_2)$$
What are $A_i, \omega_i, \phi_i$, $i=1,2$ and is there a way to get them straightforwardly (or a way to see the problem that makes it simpler)?