Question

Solve ${\tan }^{2}x+[1-\sqrt{3}]\tan x-\sqrt{3}=0$.

Answer 1

$(\tan x+1)(\tan x-\sqrt{3})=0$
$\therefore \tan x=-1=-\tan \left(\pi /4\right)=\tan (-\pi /4)$
$\therefore x=n\pi -\pi /4$
or $\tan x=\sqrt{3}=\tan \left(\pi /3\right),$
$\therefore x=n\pi +\pi /3$.