Derivation of the Sum-to-Product Formulas
To prove the sum-to-product formulas, we shall use the product-to-sum formulas. They are included below, labeled (1) through (4).
Before we begin, though, let us make a change of variables. Let us set and . We see that and .
Using these substitutions, we can now derive the sum-to-product formulas.
Formula (1) becomes:
Formula (2) becomes:
Formula (3) becomes:
Formula (4) becomes: