Question

If tan^-1x + tan^-1y + tan^-1z= pi or pi/2
then prove x+y+z=xyz or
xy +yz+zx=1

Answer 1

arctan x + arctan  y = arctan (x+y / 1-xy)

arctan (x+y / 1-xy) + arctan z = arctan (x + y + z - xyz/ 1 - xy - zx - zy)

If tan pi = 0 , then the de numerator is also 0 , solve it and you will get it

tan pie/2 = infinity, denominator = 0 , solve it and you will get it

hope this helps