Q. If $\tan^{2}{\theta - \left( 1 + \sqrt{3} \right)\tan{\theta + \sqrt{3} = 0}}$, then the general value of $\theta$ is
A) $n\pi + \frac{\pi}{4},\ n\pi + \frac{\pi}{3}$
B) $n\pi - \frac{\pi}{4},\ n\pi + \frac{\pi}{3}$
C) $n\pi + \frac{\pi}{4},\ n\pi - \frac{\pi}{3}$
D) $n\pi - \frac{\pi}{4},\ n\pi - \frac{\pi}{3}$
Explanation
(a)
Given that, $\tan^{2}{\theta - \tan{\theta - \sqrt{3}\tan{\theta + \sqrt{3} = 0}}}$
$\Rightarrow \ \tan{\theta(\tan{\theta - 1) - \sqrt{3}(\tan{\theta - 1) = 0}}}$
$\Rightarrow (\tan{\theta - \sqrt{3})\ (\tan{\theta - 1) = 0}}$
$\Rightarrow \ \theta = n\pi + \frac{\pi}{3},\ n\pi + \frac{\pi}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.