Q18 / 50 · Manipal (MET) 2023 · Mathematics
Set of values of $x$ lying in $[0,2 \pi]$ satisfying the inequality $|\sin x|\gt2 \sin ^2 x$ contains
- Correct answerA$\left(0, \frac{\pi}{6}\right) \cup\left(\pi, \frac{7 \pi}{6}\right)$
- B$\left(0, \frac{7 \pi}{6}\right)$
- C$\frac{\pi}{6}$
- DNone of these
Solution
$|\sin x|\gt2 \sin ^2 x$
$\Rightarrow|\sin x|(2|\sin x|-1) \lt 0 \Rightarrow 0 \lt |\sin x| \lt \frac{1}{2}$
$\Rightarrow x \in\left(0, \frac{\pi}{6}\right) \cup\left(\frac{5 \pi}{6}, \pi\right) \cup\left(\pi, \frac{7 \pi}{6}\right) \cup\left(\frac{11 \pi}{6}, 2 \pi\right)$
Hence, the correct answer is option: 'A'.