Is there any formula for $ \arctan x + \arctan y + \arctan z $ ?
One way to solve such type of question is to is two take two at a time and solve them.
I know the general formula for $ \arctan x + \arctan y + \arctan z = $
$ \arctan \frac{ x + y+ z - xyz }{1-xy-xz-zy} $. But what about other cases.
These cases exist in these formulas.
$ \arctan x + \arctan y = $
Case 1
If $ xy \lt 1 $
$ = \arctan\frac{ x + y }{1-xy} $
Case 2
If $ xy \gt 1 $ and $ x,y \gt 0 $
$ = \pi + \arctan\frac{ x + y }{1-xy} $
Case 3
If $ xy \gt 1$ and $ x,y \lt 0 $
$ = - \pi + \arctan\frac{ x + y }{1-xy} $
