Question

The equation $\tan x=\frac{-1}{\sqrt{3}}$ have its principal solutions as

• A. $\frac{\pi }{3}$ and $\frac{2\pi }{3}$
• B. $\frac{2\pi }{3}$ and $\frac{\pi }{4}$
• C. $\frac{5\pi }{6}$ and $\frac{11\pi }{6}$
• D. $\frac{\pi }{4}$ and $\frac{\pi }{6}$

Answer 1

Answer: (C)

We know that, $\tan \frac{\pi }{6}=\frac{1}{\sqrt{3}}$.
$\tan \left(\pi -\frac{\pi }{6}\right)=-\tan \frac{\pi }{6}=-\frac{1}{\sqrt{3}}$
and $\tan \left(2\pi -\frac{\pi }{6}\right)=-\tan \frac{\pi }{6}=-\frac{1}{\sqrt{3}}$
Thus,$\tan \frac{5\pi }{6}=\tan \frac{11\pi }{6}=-\frac{1}{\sqrt{3}}$
Therefore, principal solutions are $\frac{5\pi }{6}$ and $\frac{11\pi }{6}$.