Answer
$cot(arctan\frac{1}{x})=x$
Work Step by Step
Let $u=arctan\frac{1}{x}~~$ (Range: $-\frac{\pi}{2}\lt u\lt\frac{\pi}{2}$)
Then: $\frac{1}{x}=tan~u$
$cot(arctan\frac{1}{x})=cot~u=\frac{1}{tan~u}=x$
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