Difference of Arccotangents

Theorem

 * $\operatorname{arccot} a - \operatorname{arccot} b = \operatorname{arccot} \dfrac {a b + 1} {a - b}$

where $\operatorname{arccot}$ denotes the arccotangent.

Proof
Let $x = \operatorname{arccot} a$ and $y = \operatorname{arccot} b$.

Then:

Also see

 * Sum of Arccotangents