Simplify a expression with cos 2x

I would like to simplify the following expression :

r Cos[γ[t]] + Sqrt[l^2 - r^2/2 + 1/2 r^2 Cos[2 γ[t]]]


by using the mathematical expression :

Cos[2 x]=1 - 2 Sin[x]^2


A similar topic was already created:

How to simplify 1 - Cos[2x] to 2 Sin[x]^2?

However, I would like to use a very simple method for a Mathematica beginner.

May you advice a simple solution to obtain this kind of reduction ?

r Cos[γ[t]] + Sqrt[l^2 - r^2/2 + 1/2 r^2 Cos[2 γ[t]]] /.