Q. If $\cos{x \neq - \frac{1}{2}}$, then the solutions of $\cos{x + \cos{2x + \cos{3x = 0}}}$ are
A) $2n\pi \pm \frac{\pi}{4},\ n \in Z$
B) $2n\pi \pm \frac{\pi}{3},\ n \in Z$
C) $2n\pi \pm \frac{\pi}{6},\ n \in Z$
D) $2n\pi \pm \frac{\pi}{2},\ n \in Z$
Explanation
(a)
Given, $\cos{x + \cos{3x + \cos{2x = 0}}}$
$\Rightarrow \ 2\cos{2x\cos{x + \cos{2x = 0}}}$
$\Rightarrow \ \cos{2x\ \left( 2\cos{x + 1} \right) = 0}$
$\Rightarrow \ \cos{2x = 0\ \ \ \ \left\lbrack \because\ \cos{x \neq - \frac{1}{2}} \right\rbrack}$
$\Rightarrow \ \ \ x = \frac{\pi}{4}$
$\therefore$ General value is $2n\pi \pm \frac{\pi}{4},\ \ n \in Z$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.