Linear combination of sin and cos

[Mr Davis 97]

I have before me that $\cos 2x + \sin 2x = \sqrt{2} \cos (2x - \pi / 4)$. Where does this expression on the right come from? I tried to look on the internet but I couldn't really articulate it well enough to find anything on it.

 

[George Jones]

I have before me that $\cos 2x + \sin 2x = \sqrt{2} \cos (2x - \pi / 4)$. Where does this expression on the right come from? I tried to look on the internet but I couldn't really articulate it well enough to find anything on it.

It is easy to go from the right to the left by using the standard expansion for $\cos\left(x+y\right)$.