The value of tan (13π/12)is:

Correct option is D

Given:
$$\tan \left( \frac{13\pi}{12} \right)$$​​

Solution:

​$$\tan \left( \frac{13\pi}{12} \right)\\\ \\= \tan \left( \pi + \frac{\pi}{12} \right)\\\ \\= \tan \left( \frac{\pi}{12} \right)\\\ \\= \tan (15^\circ)\\\ \\= \tan (45^\circ - 30^\circ)\\\ \\= \frac{\tan 45^\circ - \tan 30^\circ}{1 + \tan 45^\circ \times \tan 30^\circ}\\\ \\= \frac{1 - \frac{1}{\sqrt{3}}}{1 + 1 \times \frac{1}{\sqrt{3}}}\\\ \\= \frac{\sqrt{3} - 1}{\sqrt{3} + 1} \times \frac{\sqrt{3} - 1}{\sqrt{3} - 1}\\\ \\= 2 - \sqrt{3}$$​​

Thus, the required value is $$2 - \sqrt{3} .$$​​