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 $\frac{11 \pi}{6}$.