Q. The solution set of $(5 + 4\cos{\theta)(2\cos{\theta + 1) = 0}}$ in the interval $\lbrack 0,\ 2\pi\rbrack$ is
A) $\left\{ \frac{\pi}{3},\frac{2\pi}{3} \right\}$
B) $\left\{ \frac{\pi}{3},\ \pi \right\}$
C) $\left\{ \frac{2\pi}{3},\frac{4\pi}{3} \right\}$
D) $\left\{ \frac{2\pi}{3},\frac{5\pi}{3} \right\}$
Explanation
(c)
We have, $(5 + 4\cos{\theta)(2\cos{\theta + 1) = 0}}$
$\Rightarrow \cos{\theta = - \frac{5}{4}}$ which is not possible
$\therefore\ 2\cos{\theta + 1 = 0\ \Rightarrow \ \ }\cos{\theta = - \frac{1}{2}}$
$\Rightarrow \ \theta = \frac{2\pi}{3},\frac{4\pi}{3}$
$\therefore$ Solution set is $\left\{ \frac{2\pi}{3},\frac{4\pi}{3} \right\} \in \lbrack 0,\ 2\pi\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.