Answer
$-\displaystyle \frac{\sqrt{3}}{2}$
Work Step by Step
Letting $A=2\displaystyle \theta, \quad \cos A=\frac{1}{2}$
we express $\displaystyle \theta=\frac{A}{2},\quad\cos\theta=\cos\frac{A}{2}$
($\cos\theta$ is negative as $\theta$ terminates in Q.II.)
Half-Angle identity:
$\cos\theta$=$\displaystyle \cos\frac{A}{2}=-\sqrt{\frac{1+\cos A}{2}}=-\sqrt{\frac{1+\frac{1}{2}}{2}}$
$=-\displaystyle \sqrt{\frac{3}{4}}=-\frac{\sqrt{3}}{2}$