If -1-sin x-1-sin x-23- then x lies in

|1 |sin x|1+|sin x||≥23 ⇒1|1+|sin x||≥23 ⇒ nbsp; 11+|sin x|≥23 (∵ 1+|sin x|≥1) ⇒ |sin x|≤12 From the graph, nbsp; [ π6,π6], [5π6,7π6], [ 7π6, 5π6] ...

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Standard XII

Mathematics

General Solution of Trigonometric Equation

If |1-|sin x|...

Question

If $∣ ∣ ∣ 1 - \frac{| sin x |}{1 + | sin x |} ∣ ∣ ∣ \geq \frac{2}{3}$ , then $x$ lies in

[- \frac{π}{6}, \frac{π}{6}]

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[\frac{5 π}{6}, \frac{7 π}{6}]

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[- \frac{7 π}{6}, - \frac{5 π}{6}]

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[\frac{π}{6}, \frac{5 π}{6}]

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Solution

The correct option is C $[- \frac{7 π}{6}, - \frac{5 π}{6}]$
$∣ ∣ ∣ 1 - \frac{| sin x |}{1 + | sin x |} ∣ ∣ ∣ \geq \frac{2}{3} \Rightarrow \frac{1}{| 1 + | sin x | |} \geq \frac{2}{3} \Rightarrow \frac{1}{1 + | sin x |} \geq \frac{2}{3} (∵ 1 + | sin x | \geq 1) \Rightarrow | sin x | \leq \frac{1}{2}$

From the graph,
$[- \frac{π}{6}, \frac{π}{6}], [\frac{5 π}{6}, \frac{7 π}{6}], [- \frac{7 π}{6}, - \frac{5 π}{6}]$

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General Solution of Trigonometric Equation

Standard XII Mathematics

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If ∣∣∣1−|sinx|1+|sinx|∣∣∣≥23, then x lies in

The correct option is C [−7π6,−5π6]∣∣∣1−|sinx|1+|sinx|∣∣∣≥23⇒1|1+|sinx||≥23⇒11+|sinx|≥23 (∵1+|sinx|≥1)⇒|sinx|≤12 From the graph, [−π6,π6],[5π6,7π6],[−7π6,−5π6]

If $∣ ∣ ∣ 1 - \frac{| sin x |}{1 + | sin x |} ∣ ∣ ∣ \geq \frac{2}{3}$ , then $x$ lies in