Proof of sum to product formula
From the product to sum formula:
2sin A cos B = sin (A + B) + sin (A − B)
Let A + B = C A − B = D Adding 2A = C + D A = Subtracting 2B = C − D B =
Let A + B = C A − B = D
Adding 2A = C + D
A =
Subtracting 2B = C − D
B =
Substituting into: 2sin A cos B = sin (A + B) + sin (A − B)
sin C + sin D = 2sin cos
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