Answer
$\dfrac{1}{4}$
Work Step by Step
Substitute $\frac{\pi}{6}$ to $x$ to obtain:
$\frac{1}{2}\cos{(2x)}= \frac{1}{2}\cos{[2(\frac{\pi}{6})]}=\frac{1}{2}\cos{(\frac{\pi}{3})}$
$\dfrac{\pi}{3}$ is a special angle whose cosine value is $\dfrac{1}{2}$.
Thus, when $x=\frac{\pi}{6}$,
$\dfrac{1}{2}\cos{(2x)} = \dfrac{1}{2} \cdot \dfrac{1}{2}=\dfrac{1}{4}$
