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Find the exact value for $\cos { 75 }^{ \circ }$ by using the half angle formula.

A

$-\cfrac{\sqrt{2-\sqrt{3}}}{4}$

B

${\sqrt{2-\sqrt{3}}}$

C

$-\cfrac{\sqrt{2-\sqrt{3}}}{2}$

D

$\cfrac{\sqrt{2-\sqrt{3}}}{2}$

E

$\cfrac{\sqrt{2-\sqrt{3}}}{4}$

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