Question

Solve $\cot \theta +\tan \theta =2cosec\theta$.

Answer 1

$\frac{\cos \theta }{\sin \theta }+\frac{\sin \theta }{\cos \theta }=\frac{2}{\sin \theta }$
or $\frac{{\cos }^2\theta +{\sin }^2\theta }{\sin \theta \cos \theta }=\frac{2}{\sin \theta }$
or $\frac{1}{\sin \theta \cos \theta }=\frac{2}{\sin \theta }$
$\therefore \cos \theta =\frac{1}{2}$ $(\sin \theta \ne 0)$
$\therefore \theta =2n\pi \pm \pi /3$.