Q. If $\frac{1 - \cos{2\theta}}{1 + \cos{2\theta}} = 3$, then the general value of $\theta$ is
A) $2n\pi \pm \frac{\pi}{6}$
B) $n\pi \pm \frac{\pi}{6}$
C) $2n\pi \pm \frac{\pi}{3}$
D) $n\pi \pm \frac{\pi}{3}$
Explanation
(d)
Given that, $\frac{1 - \cos{2\theta}}{1 + \cos{2\theta}} = 3$
$\Rightarrow \ \frac{2\sin^{2}\theta}{2\cos^{2}\theta} = 3$
$\Rightarrow \ \tan^{2}{\theta = \left( \ \sqrt{3} \right)^{2}}$
$\Rightarrow \ \tan^{2}\theta = \tan^{2}\frac{\pi}{3}\$
$\Rightarrow \ \theta = n\pi \pm \frac{\pi}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.