# How to Express Products of Trigonometric Functions as Sums or Differences

If you can break up a product of trig functions into the sum of two different terms, each with its own trig function, doing the math becomes much easier. In pre-calculus, problems of this type usually say “express the product as a sum or difference.” In the following example, you’ll make the conversion from a product to a sum.

You have three product-to-sum formulas to digest: sine multiplied by cosine, cosine multiplied by cosine, and sine multiplied by sine.

Suppose that you’re asked to express 6 cos *q* sin 2*q* as a sum. Rewrite this expression as 6 sin 2*q* cos *q* (thanks to the commutative property) and then plug what you know into the formula to get

For example, to express

as a sum, rewrite it as the following:

To express sin 5*x* cos 4*x* as a sum, rewrite it as the following: