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JEE MATHEMATICS MCQ: FUNCTIONS

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The domain of the function f(x)=cosec−1[sin⁡x]f\left( x \right) = \mathrm{cose}{\mathrm{c}^{ - 1}}\left[ {\sin x} \right] in [0,  2  π],\left[ {0,\;2\;\pi } \right], where [⋅]\left[ \cdot \right] denotes the greatest integer function, is
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Correct option: B
(π,2  π)∪{π/2}\left( {\pi ,2\;\pi } \right) \cup \left\{ {\pi /2} \right\}
Option B ((π,2  π)∪{π/2}\left( {\pi ,2\;\pi } \right) \cup \left\{ {\pi /2} \right\}) is correct because it identifies the intervals where [sin x] is either 1 or -1, which are the only values for which csc-1[sin x] is defined.

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