Answer
$3$
Work Step by Step
Let $csc^{-1}\sqrt {10}=t$, we have $csc(t)=\sqrt {10}, sin(t)=\frac{1}{\sqrt {10}}, cos(t)=\frac{3}{\sqrt {10}}$, thus $cot(csc^{-1}\sqrt {10})=cot(t)=3$
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