Q. The solutions of the equation $4\cos^{2}{x + 6\sin^{2}{x = 5}}$ are
A) $x = n\pi \pm \frac{\pi}{4}$
B) $x = n\pi \pm \frac{\pi}{3}$
C) $x = n\pi \pm \frac{\pi}{2}$
D) $x = n\pi \pm \frac{2\pi}{3}$
Explanation
(a)
Given, $4\cos^{2}{x + 6\sin^{2}{x = 5}}$
$\Rightarrow \ \ 4\left( \cos^{2}{x + \sin^{2}x} \right) + 2\sin^{2}{x = 5}$
$\Rightarrow \ 2\sin^{2}{x = 5 - 4}$
$\Rightarrow \ \sin{x = \pm \frac{1}{\sqrt{2}}}$
$\therefore\ \ \ x = n\pi \pm \frac{\pi}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.