Answer
$sin~\frac{\pi}{12}~cos~\frac{\pi}{4}+cos~\frac{\pi}{12}~sin~\frac{\pi}{4}=\frac{\sqrt 3}{2}$
Work Step by Step
$sin(u+v)=sin~u~cos~v+cos~u~sin~v$
$sin~\frac{\pi}{12}~cos~\frac{\pi}{4}+cos~\frac{\pi}{12}~sin~\frac{\pi}{4}=sin(\frac{\pi}{12}+\frac{\pi}{4})=sin(\frac{\pi}{12}+\frac{\pi(3)}{4(3)})=sin(\frac{\pi}{12}+\frac{3\pi}{12})=sin~\frac{4\pi}{12}=sin~\frac{\pi}{3}=\frac{\sqrt 3}{2}$
