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