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What is $\tan \left(\frac{\pi}{12}\right)$ equal to?
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The correct answer is:
$2-\sqrt{3}$
$\quad \tan \frac{\pi}{12}=\tan \left(\frac{\pi}{3}-\frac{\pi}{4}\right)=\frac{\tan \pi / 3-\tan \pi / 4}{1+\tan \pi / 3 \tan \pi / 4}$
$=\frac{\sqrt{3}-1-3+\sqrt{3}}{(1)^{2}-(\sqrt{3})^{2}}=\frac{2(\sqrt{3}-2)}{-2}=2-\sqrt{3}$
$=\frac{\sqrt{3}-1-3+\sqrt{3}}{(1)^{2}-(\sqrt{3})^{2}}=\frac{2(\sqrt{3}-2)}{-2}=2-\sqrt{3}$
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