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Find the exact value for $\cos { 105 }^{ \circ }$ by using the angle addition or subtraction formula for cosine.

A

$\cfrac{\sqrt{2}-\sqrt{6}}{2}$

B

$\cfrac{-\sqrt{2}-\sqrt{6}}{4}$

C

$\cfrac{\sqrt{2}+\sqrt{6}}{4}$

D

$\cfrac{\sqrt{6}-\sqrt{2}}{4}$

E

$\cfrac{\sqrt{2}-\sqrt{6}}{4}$

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