#### Answer

$\dfrac {\sqrt {2}}{4}\left( 1-\sqrt {3}\right) $

#### Work Step by Step

$\cos \left( -\dfrac {7\pi }{12}\right) =\cos \left( \left( -\dfrac {\pi }{3}\right) +\left( -\dfrac {\pi }{4}\right) \right) =\cos \left( -\dfrac {\pi }{3}\right) \cos \left( -\dfrac {\pi }{4}\right) -\sin \left( -\dfrac {\pi }{3}\right) \sin \left( -\dfrac {\pi }{4}\right)=\dfrac {1}{2}\times \dfrac {\sqrt {2}}{2}-\dfrac {\sqrt {3}}{2}\times \dfrac {\sqrt {2}}{2}=\dfrac {\sqrt {2}}{4}\left( 1-\sqrt {3}\right) $