Q. Set of values of $x$ lying in $\lbrack 0,\ 2\pi\rbrack$ satisfying the inequality $|\sin{x| > 2\sin^{2}x}$ contains
A) $\left( \ 0,\frac{\pi}{6} \right) \cup \left( \ \pi,\frac{7\pi}{6} \right)$
B) $\left( 0,\frac{7\pi}{6} \right)$
C) $\frac{\pi}{6}$
D) None of these
Explanation
(a)
$|\sin{x| > 2\sin^{2}x}$
$\Rightarrow |\sin{x|(2|\sin{x| - 1) < 0}}$
$\Rightarrow \ 0 < |\sin{x| < \frac{1}{2}}$
$\Rightarrow \ x \in \left( \ 0,\frac{\pi}{6} \right) \cup \left( \frac{5\pi}{6},\ \pi \right) \cup \left( \pi,\frac{7\pi}{6} \right) \cup \left( \frac{11\pi}{6},\ 2x \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.