What is the value of $\cos 75^{\circ}$ ?

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$2 \sqrt{2}$

$\frac{\sqrt{3} + 1}{2 \sqrt{2}}$

$\frac{\sqrt{3} - 1}{2 \sqrt{2}}$

answer is B.

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Detailed Solution

$c o s 75^{\circ} = c o s (45 ° + 30 °) = \cos 45 ° \cos 30 ° - \sin 45 ° \sin 30 ° = \frac{1}{\sqrt{2}} \times \frac{\sqrt{3}}{2} - \frac{1}{\sqrt{2}} \times \frac{1}{2} = \frac{\sqrt{3} - 1}{2 \sqrt{2}}$

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