Question

Find the solution of following equation
$2\tan \theta -\cot \theta +1=0$ then $tan\theta =\frac{m}{n}$ and $tan\theta =p$ then m+n+p =

Answer 1

Put $\text{cot}\theta$ as $\frac{1}{\tan \theta }$

$⟹2\tan \theta -\frac{1}{\tan \theta }+1=0$

put $\tan \theta =x$

$⟹2x^2+x-1=0⟹x=\frac{1}{2},-1$

$⟹\tan \theta =-1⟹\theta =\frac{3\pi }{4}$

$⟹\tan \theta =\frac{1}{2}⟹\theta ={\text{tan}}^{-1}\frac{1}{2}$