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