Question

The value of $\tan \left(\frac{\pi }{12}\right)$ is equal to

• A. $4-2\sqrt{3}$
• B. $4+2\sqrt{3}$
• C. $2+\sqrt{3}$
• D. $2-\sqrt{3}$

Answer 1

The correct option is D $2-\sqrt{3}$

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