Answer
$\frac{\sqrt 2}{2}$
Work Step by Step
The Product-Sum Formula seems to fit the expression, but we need to find the other angle first.
The formula states $sin(A+B)=sinAcosB+cosAsinB$, let $B=\frac{\pi}{12}$ and $A=\frac{\pi}{6}$, we have
$\frac{1}{2}cos\frac{\pi}{12}+\frac{\sqrt 3}{2}sin\frac{\pi}{12}=sin\frac{\pi}{6}cos\frac{\pi}{12}+cos\frac{\pi}{6}sin\frac{\pi}{12}=sin(\frac{\pi}{6}+\frac{\pi}{12})=sin\frac{3\pi}{12}=sin\frac{\pi}{4}=\frac{\sqrt 2}{2}$
