# 8.3b. The reverse of the factor formula

Example question:

### Reversing the factor formula

The factor formulas are provided in the formula list MF26:

These formulas allow us to convert addition/subtraction of sine/cosine functions to a product. While this may be useful for other applications, integration of a product is not something we can perform generally.

Instead, we wish to reverse the formula: given a product of sine/cosine functions, we hope to convert them to addition/subtraction since we can integrate sums and differences separately.

The trick is to let $\frac{1}{2} (P+Q)$ be $A$ and $\frac{1}{2} (P-Q)$ be $B$. Then it can be easily shown that $A+B = P$ and $A-B = Q$. This gives us

Applying this to our question gives us