# Where does this trig identiy come from?

1. Apr 12, 2012

### vincent_vega

Our teacher used the following on a problem solution:

cos(x-a)cos(b-x) = $\frac{1}{2}$[cos(a+b-2x) + cos(a-b)]

Where does this come from? I can't find it in anywhere (except for wolframalpha). Thanks.

Last edited: Apr 12, 2012
2. Apr 12, 2012

### Staff: Mentor

3. Apr 12, 2012

### vincent_vega

It comes from the known identity for sum of cosines: $\cos \alpha+\cos\beta=2\cos\frac{\alpha+\beta}{2} \cos \frac{\alpha-\beta}{2}$