Answer
$\dfrac{4+\sqrt3}{2}$
Work Step by Step
Substitute $\frac{\pi}{6}$ to $x$ to obtain:
$2+\cos{x}= 2+\cos{(\frac{\pi}{6})}$
$\dfrac{\pi}{6}$ is a special angle whose cosine value is $\dfrac{\sqrt3}{2}$.
Thus, when $x=\frac{\pi}{6}$,
$2+\cos{x} = 2+ \dfrac{\sqrt3}{2}=\dfrac{4}{2} + \dfrac{\sqrt3}{2} = \dfrac{4+\sqrt3}{2}$
