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Find the exact $\cos{\cfrac{5\pi}{8}}$ by using the half angle formula for cosine.

A

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

B

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

C

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

D

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

E

$$\cfrac{\sqrt{2}}{2}-1$$

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