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Set of value of x lying in $[0, 2 π]$ satisfying the inequality $| \sin x | > 2 \sin^{2} x$ contains

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$(0, \frac{π}{6}) \cup (π, \frac{7 π}{6})$

$(0, \frac{7 π}{6})$

${\frac{π}{6}}$

$(0, \frac{π}{6}) \cup (\frac{5 π}{6}, π) \cup (π, \frac{7 π}{6}) \cup (\frac{11 π}{6}, 2 π)$

answer is D.

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Detailed Solution

(4) $| \sin x | > 2 \sin^{2} x$
$\Rightarrow | \sin x | (2 | \sin x | - 1) < 0$
$\Rightarrow 0 < | \sin x | < \frac{1}{2}$ , then draw the graph

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