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  4. The value of tan (13 π/12) is

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Q. The value of $\tan \frac{13 \pi}{12}$ is

Trigonometric Functions

Solution:

We have,
$\tan \frac{13 \pi}{12} =\tan \left(\pi+\frac{\pi}{12}\right)=\tan \frac{\pi}{12}=\tan \left(\frac{\pi}{4}-\frac{\pi}{6}\right)$
$ =\frac{\tan \frac{\pi}{4}-\tan \frac{\pi}{6}}{1+\tan \frac{\pi}{4} \tan \frac{\pi}{6}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}=\frac{\sqrt{3}-1}{\sqrt{3}+1}=2-\sqrt{3}$