Question

Find the principal solutions of the equation $\tan x=-\frac{1}{\sqrt{3}}.$

Answer 1

Given data : $\tan x=-\frac{1}{\sqrt{3}}$

We know $-\tan \frac{\pi }{6}=-\frac{1}{\sqrt{3}}$
Here $\tan x$ is negative.
$\tan x$ is negative in $2^{nd}$ and $4^{th}$ quadrant.

Value in $2^{nd}$ quadrant $=\pi -\frac{\pi }{6}=\frac{5\pi }{6}$
Value in $4^{nd}$ quadrant $=2\pi -\frac{\pi }{6}=\frac{11\pi }{6}$

$\therefore$ Principal solutions are $x=\frac{5\pi }{6}$ and $\frac{11\pi }{6}$