Question

Solve ${\tan }^2\theta +2\sqrt{3}\tan \theta =1$

Answer 1

Given, ${\tan }^2\theta +2\sqrt{3}\tan \theta =1$
$\Rightarrow \tan \theta =\frac{-2\sqrt{3}\pm \sqrt{12+4}}{2}=-\sqrt{3}\pm 2$
$\Rightarrow \theta =n\pi +\frac{\pi }{12}$ or $\theta =n\pi -\frac{5\pi }{12}$