Welcome to the forum.
I hung on hoping someone who knows the answer would post, but it doesn't look like they will so I'll jump in with what little I know . Maybe that will spur someone else to tell me I'm wrong and then we'll get somewhere.
The first result comes from this trig formula
http://www.sosmath.com/trig/prodform/prodform.html
So it works because the amplitudes are the same.
I'm fairly certain there's no formula when the amplitudes are different. There might be one when one amplitude is a simple factor of the other.
Bob
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