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Find the exact value for $\cos { 15 }^{ \circ }$ by using the half-angle formula.

A

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

B

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

C

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

D

$\sqrt{2+\sqrt{3}}$

E

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

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