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

Answer 1

Answer: (C)

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