The domain of the function 11+2sin⁡x is

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R=nπ+−1n7π6,n∈z

R=nπ+−1n3π6,n∈z

R=nπ+−1n5π6,n∈z

R=nπ+−1nπ6,n∈z

answer is A.

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Detailed Solution

To definef (x), we must have 1+2sin⁡x≠0 or sin⁡x≠−12 or x≠nπ+(−1)n7π6,n∈ZHence, the domain of the function isR−nπ+(−1)n7π6,n∈Z

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