Answer
$\dfrac{\sqrt{2-\sqrt{3}}}{2}$
Work Step by Step
$\cos{\dfrac{A}{2}} = \sqrt{\dfrac{1+\cos{A}}{2}}$
$\cos{75} = \sqrt{\dfrac{1+\cos{150}}{2}} = \sqrt{\dfrac{1-\dfrac{\sqrt{3}}{2}}{2}}$
$\cos{75} = \dfrac{\sqrt{2-\sqrt{3}}}{2}$
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