Question

if tan-1x+tan-1y+tan-1z=π/2 show that xy+yz+zx=1?

Answer 1

Here is your answer.
tan-1x+tan-1y+tan-1z =π/2
then,tan^-1x (x+y+z-xyz)/1-xy-yz-zx=π/2
(x+y+z-xyz)/1-xy-yz-zx =tanπ/2
(x+y+z-xyz)/1-xy-yz-zx =1/0
1×(1-xy-yz-zx)=(x+y+z-xyz)×0
1-xy-yz-zx=0
xy+yz+zx=1....Proved.