Answer
$\frac{1+\sqrt{3}}{2\sqrt2}$
Work Step by Step
Using the given identities and the known values: $\cos (\pi/12)=\pm\sqrt{\frac{1+\cos(\pi/6)}{2}}=\sqrt{\frac{1+(\frac{\sqrt3}{2})}{2}}=\frac{1+\sqrt{3}}{2\sqrt2}$
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