Answer
The derivation is shown below.
Work Step by Step
Using double angle formula of cosine function, we get
$\cos^2(x)=\dfrac{1+\cos 2x}{2}$
Now, substitute $y=\dfrac{\theta}{2}$ to obtain
$\cos^2 \dfrac{\theta}{2}=\dfrac{1+\cos 2\cdot\dfrac{\theta}{2}}{2}$
$\implies \cos^2\dfrac{\theta}{2}=\dfrac{1+\cos\theta}{2}$, which is the required formula.
