Answer
$\pm \sqrt{\dfrac{1+\cos{\theta}}{2}}$
Work Step by Step
Using the double angle formula:
$$\cos{2A} = 2 \cos^2{A}-1$$
$$2\cos^2{A} = \cos{2A}+1$$
$$\cos^2{A} = \dfrac{1+\cos{2A}}{2}$$
$$\cos{A} = \pm \sqrt{\dfrac{1+\cos{2A}}{2}}$$
Replacing $A$ with $\dfrac{\theta}{2}$:
$\cos{\dfrac{\theta}{2}} = \pm \sqrt{\dfrac{1+\cos{\theta}}{2}}$
