Trigo “Sum to Product” formula is given in the math formula list MF26. However, “Product to Sum” formula is not in the formula list. Yet, students are often required to use the “Product to Sum” formula in mathematical induction or integration. Hence, knowing how to derive the “Product to Sum” formula from “Sum to Product” formula is critical.

“Sum to Product” formula

To derive the “Product to Sum” formula

Let P = X+Y and Q= X-Y

Substitute into the “Sum to Product” formula, we derived the “Product to Sum” formula

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