Q. If $\tan{2\theta\tan{\theta = 1}}$, then the general value of $\theta$ is
A) $\left( \ n + \frac{1}{2} \right)\frac{\pi}{3}$
B) $\left( \ n + \frac{1}{2} \right)\pi$
C) $\left( 2n \pm \frac{1}{2} \right)\frac{\pi}{3}$
D) None of these
Explanation
(a)
We have, $\tan{2\theta\tan{\theta = 1\ \Rightarrow}\ }\tan{2\theta{= cot}\theta}$
$= \tan\left( \frac{\pi}{2} - \theta \right)$
$\Rightarrow \ 2\theta = n\pi + \frac{\pi}{2} - \theta$
$\Rightarrow \ \theta = \frac{n\pi}{3} + \frac{\pi}{6}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.