Which of the following is equivalent to ${\csc }^{-1}\left(y\right)$ for $y\ne 0$?

• A. ${\sin }^{-1}\left(\frac{1}{y}\right)$
• B. ${\cos }^{-1}\left(\frac{1}{y}\right)$
• C. ${\tan }^{-1}\left(\frac{1}{y}\right)$
• D. ${\cot }^{-1}\left(\frac{1}{y}\right)$