Difference of Arccotangents

Theorem

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

where $\arccot$ denotes the arccotangent.

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

Then:

Also see

 * Sum of Arccotangents