Answer
$\frac{|u|}{u\sqrt {u^2-1}}$
Work Step by Step
Let $csc^{-1}(u)=t$, we have $csc(t)=u$ or $sin(t)=\frac{1}{u}$, thus $cos(t)=\sqrt {1-sin^2(t)}=\frac{\sqrt {u^2-1}}{|u|}$ and $tan(t)=\frac{|u|}{u\sqrt {u^2-1}}$
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.