Identity question

1. May 25, 2012

ZedCar

1. The problem statement, all variables and given/known data

In a worked example I have of an integration it states the integral of (cosx)^2 = the integral of (1 + cos2x)/2

How is this equality reached?

Is this a known identity, (cosx)^2 = (1 + cos2x)/2 ?

Thank you.

2. Relevant equations

3. The attempt at a solution

2. May 25, 2012

Karamata

Yes.

3. May 25, 2012

Whovian

Yep, that's a very well-known identity, derived from very simple algebra from $\cos\left(2\cdot x\right)=2\cdot\cos^2\left(x\right)-1$

4. May 25, 2012

tiny-tim

cos(x + x) = … ?