Question

Solve the equation:-
$2tan\theta -cot\theta =-1$

Answer 1

$2\tan \theta -\frac{1}{\tan \theta }=-1$

$\Rightarrow 2{\tan }^2\theta +\tan \theta -1=0$

$\Rightarrow 2{\tan }^2\theta +2\tan \theta -\tan \theta -1=0$

$\Rightarrow 2\tan \theta (\tan \theta +1)-(\tan \theta +1)=0$

$\Rightarrow (\tan \theta +1)(2\tan \theta -1)=0$

$\Rightarrow \tan \theta =-1,\frac{1}{2}$

$\therefore \theta =-\frac{\pi }{4},\frac{3\pi }{4},{\tan }^{-1}\left(\frac{1}{2}\right)$