Answer:
Option A
Explanation:
Since x,y and z are in AP
$\therefore$ 2y=x+z
also tan-1x, tan-1y and tan-1 z are in AP
$\therefore$ 2 tan-1y=tan-1x= tan-1 (z)
$ \Rightarrow$ $ \tan^{-1}\left(\frac{2y}{1-y^{2}}\right)=\tan^{-1} \left(\frac{x+z}{1-xz}\right)$
$ \Rightarrow$ $ \left(\frac{x+z}{1-y^{2}}\right)= \left(\frac{x+z}{1-xz}\right)\Rightarrow y^{2}=xz$ Since x,y and z are in AP as well as in GP
$\therefore$ x=y=z
