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

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

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

$\sqrt{3} + 1$

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

answer is D.

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Detailed Solution

$\tan 75^{\circ} = \tan (45 ° + 30 °) = \frac{\tan 45 ° + \tan 30 °}{1 - \tan 45 ° \tan 30 °} = \frac{1 + \frac{1}{\sqrt{3}}}{1 - 1 \times \frac{1}{\sqrt{3}}} = \frac{\sqrt{3} + 1}{\sqrt{3} - 1}$

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