Answer
$\dfrac {\sqrt {2}}{4}\left( \sqrt {3}-1\right) $
Work Step by Step
$\sin \dfrac {\pi }{12}=\sin \left( \dfrac {\pi }{3}-\dfrac {\pi }{4}\right) =\sin \dfrac {\pi }{3}\cos \dfrac {\pi }{4}-\cos \dfrac {\pi }{3}\sin \dfrac {\pi }{4}=\dfrac {\sqrt {3}}{2}\dfrac {\sqrt {2}}{2}-\dfrac {1}{2}\dfrac {\sqrt {2}}{2}=\dfrac {\sqrt {2}}{4}\left( \sqrt {3}-1\right) $