Question

Solve $1-2\sin \theta -2\cos \theta +\cot \theta =0$, $(0<\theta <2\pi )$.

Answer 1

$(\cos \theta +\sin \theta )[\frac{1}{\sin \theta }-2]=0$
$\therefore \sin \theta =\frac{1}{2},\tan \theta =-1=\tan (-\frac{\pi }{4})$
$\therefore \theta =\frac{\pi }{6},\pi -\frac{\pi }{6},\pi +(-\frac{\pi }{4}),2\pi +(-\frac{\pi }{4})$
$\therefore \theta =\frac{\pi }{6},\frac{5\pi }{6},\frac{3\pi }{4},\frac{7\pi }{4}$ in the given range.