Q. The equation $3\sin^{2}{x + 10\cos{x - 6 = 0}}$ is satisfied, if
A) $x = n\pi \pm \cos^{- 1}\left( \frac{1}{3} \right)$
B) $x = 2n\pi \pm \cos^{- 1}\left( \frac{1}{3} \right)$
C) $x = n\pi \pm \cos^{- 1}\left( \frac{1}{6} \right)$
D) $x = 2n\pi \pm \cos^{- 1}\left( \frac{1}{6} \right)$
Explanation
(b)
Given, $3\sin^{2}{x + 10\cos{x - 6 = 0}}$
$\Rightarrow \ \ 3\left( 1 - \cos^{2}x \right) + 10\cos{x - 6 = 0}$
$\Rightarrow \ \ - 3\cos^{2}{x + 10\cos{x - 3 = 0}}$
$\Rightarrow \ \ \left( \cos{x - 3} \right)\left( 1 - 3\cos x \right) = 0$
$\Rightarrow \ \cos{x \neq 3}$ or $\cos{x = \frac{1}{3}}$
$\Rightarrow \ \ x = 2n\pi \pm \cos^{- 1}\left( \frac{1}{3} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.