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What is the domain of validity for csc theta = 1 / sin theta?

AAll real numbers
BAll real numbers except odd multiples of pi/ 2
CAll real numbers except even multiples of pi/2
DAll real numbers except multiples of pi.

Verified Answer :

\(De finition\ of\ csc\theta=\frac{1}{sin\theta}\\-----------------------\\therefore\ csc\theta=\frac{1}{sin\theta}\to\frac{1}{sin\theta}=\frac{1}{sin\theta}\\\\the\ denominator\ must\ be\ different\ from\ zero,\ therefore\\\\sin\theta eq0\iff\theta eq k\pi\ where\ k\in\mathbb{Z}\\\\Answer:\boxed{D}\)

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