Sum 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

 * Difference of Arccotangents