Solving Identity Question: (cosx)^2 = (1 + cos2x)/2

[ZedCar]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

 

[Karamata]

Yes.

 

[Whovian]

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

 

[tiny-tim]

cos(x + x) = … ?