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The domain of the function $f (x) = \sqrt{\log (\frac{1}{|\sin x|})}$

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R--π,π

R-nπ|n∈Z

R-2nπ|n∈z

-∞,∞

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detailed solution

Correct option is B

fx is defined for log1sinx≥0or 1sinx≥1 and sinx≠0or sinx≠0 1sinx≥1 for all xor x≠nπ, n∈ZHence, the domain of fx is R-nπ. n∈Z.

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The domain of the function fx=log1sinx

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The domain of the function $f (x) = \sqrt{\log (\frac{1}{|\sin x|})}$