Question

Find the principal solution of the following equation:
$\tan x=\sqrt{3}$

• A. $x=\frac{\pi }{3}$ and $x=\frac{4}{3}\pi$
• B. $x=\frac{\pi }{2}$ and $x=\frac{1}{3}\pi$
• C. $x=\frac{\pi }{4}$ and $x=\frac{2}{3}\pi$
• D. $x=3$ and $x=\frac{4}{3}\pi$

Answer 1

The correct option is A $x=\frac{\pi }{3}$ and $x=\frac{4}{3}\pi$

We have,

$\tan x=\sqrt{3}$

$\tan x=\tan \left(\frac{\pi }{3}\right)$

$x=\pi /3------e{q}^n\left(1\right)$

Put again equation

$\tan x=\tan (\pi +\frac{\pi }{3})$

$x=\frac{4\pi }{3}------e{q}^n\left(2\right)$

From equation $\left(1\right)$ and $\left(2\right)$

$x=\frac{\pi }{3},\frac{4\pi }{3}$

Hence this is the answer.