A) \[\underset{n\in I}{\mathop{\bigcup }}\,\left( 2n\pi ,2n\pi +\frac{\pi }{2} \right)\]
B) \[\underset{n\in I}{\mathop{\bigcup }}\,[2n\pi ,\,(2n+1)\pi ]\]
C) \[\underset{n\in I}{\mathop{\bigcup }}\,[(2n-1)\pi ,2n\pi ]\]
D) None of these
Correct Answer: B
Solution :
\[\frac{1}{\sin x}-1\ge 0;\] \[\frac{1-\sin x}{\sin x}\ge 0\] \[\frac{\sin x-1}{\sin x}\le 0\Rightarrow 0<\sin x\le 1\] \[\Rightarrow \,\,x\in \underset{n\in I}{\mathop{\bigcup }}\,[2n\pi ,(2n+1)\pi ]\]
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