Answer
$\dfrac{\sqrt{2+\sqrt{3}}}{2}$
Work Step by Step
$\cos{\dfrac{A}{2}} = \sqrt{\dfrac{1+\cos{A}}{2}}$
$\cos{15} =\sqrt{\dfrac{1+\cos{30}}{2}} = \sqrt{\dfrac{1+\dfrac{\sqrt{3}}{2}}{2}}$
$\cos{15} = \dfrac{\sqrt{2+\sqrt{3}}}{2}$
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