Emulating 2 frequencies with one amp modulated osc

So, I’m trying to take two cv/gate pairs and synthesize them with one cv/gate pair. But I'm not getting it:

in math terms that would mean translating this:
a=sin(f0 *t) * a0 + sin(f1 + t) * a1

and translating it to

a = sin( somefunction(t)) * anotherfunction(t)

I know you can calculate beat frequencies but it doesn't account for the amplitudes or the little phase flip that happens when you actually combine two sine waves at the same amplitude. Also, the modulator doesn't always look symmetrical.

what say you maxers ?