Answer
$\pm \sqrt {csc^{2}x-1}$
Work Step by Step
$\cot x=\dfrac {\cos x}{\sin x}=\pm \dfrac {\sqrt {1-\sin ^{2}x}}{\sin x}=\pm \sqrt {\dfrac {1}{\sin ^{2}x}-1}=\pm \sqrt {csc^{2}x-1}$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.