#### Answer

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

#### Work Step by Step

$\cos \left( -105\right) =\cos \left( -60-45\right) =\cos (-60)\cos (-45)+\sin (-60)\sin (-45)=\dfrac {1}{2}\times \dfrac {\sqrt {2}}{2}+\left( -\dfrac {\sqrt {3}}{2}\right) \times \left( -\dfrac {\sqrt {2}}{2}\right) =\dfrac {\sqrt {2}}{4}\left( 1+\sqrt {3}\right) $