Answer
$- \sqrt{\dfrac{2-\sqrt{3}}{4}}$
Work Step by Step
$\cos{\dfrac{A}{2}} = \pm \sqrt{\dfrac{1+\cos{A}}{2}}$
$\cos{105} = - \sqrt{\dfrac{1+\cos{210}}{2}} = -\sqrt{\dfrac{1-\dfrac{\sqrt{3}}{2}}{2}}$
$\cos{105} = - \sqrt{\dfrac{2-\sqrt{3}}{4}}$