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${cosec}^{- 1} (\cos x)$ is defined if

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x∈[−1, 1]

x∈R

x=(2n+1)π2,n∈Z

x=nπ,n∈Z

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detailed solution

Correct option is D

We know that cosec−1⁡x is defined forx∈(−∞, −1]∪[1, ∞). Therefore, cosec−1⁡(cos⁡x) is defined forcos⁡x=±1⇒x=nπ, n∈Z.

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cosec−1⁡(cos⁡x) is defined if

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${cosec}^{- 1} (\cos x)$ is defined if