If Tan−1x,Tan−1y,Tan−1z are in A.P then 2y1−y2=
x−z1+xz
x+z
xz
x+z1−xz
Tan-1x, Tan-1y, Tan-1z are in A.P.
⇒2Tan−1y=Tan−1x+Tan−1z⇒Tan−12y1−y2=Tan−1x+z1−xz⇒2y1−y2=x+z1−xz