Question

If $\cot \theta +\tan \theta =2cosec\theta$, the general value of $\theta$ is

• A. $n\pi \pm \frac{\pi }{3}$
• B. $n\pi \pm \frac{\pi }{6}$
• C. $2n\pi \pm \frac{\pi }{3}$
• D. $2n\pi \pm \frac{\pi }{6}$

Answer 1

Answer: (C)

$\cot \theta +\tan \theta =2cosec\theta$
$\Rightarrow \frac{1}{\sin \theta \cos \theta }=\frac{2}{\sin \theta }$
$\Rightarrow \cos \theta =\frac{1}{2}=\cos \left(\frac{\pi }{3}\right)$
$\Rightarrow \theta =2n\pi \pm \frac{\pi }{3}$