#### Answer

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

#### Work Step by Step

$\cos 75=\cos \left( 45+30\right) =\cos 45\cos 30-\sin {45}\sin {30}=\dfrac {\sqrt {2}}{2}\times \dfrac {\sqrt {3}}{2}-\dfrac {\sqrt {2}}{2}\times \dfrac {1}{2}=\dfrac {\sqrt {2}}{2}\left( \sqrt {3}-1\right) $