Question

prove that arctan (x) + arctan (y) =(x+y)/(1-xy)
(i have solved this part by using the tangent sum formula)
the part i am stuck on is this

use this relationship to show that if

arctan (x) + arctan (y) + arctan (z) = pi/2

then xy + yz +zx =1

Answer 1

after substitution and elimination i have got this equation'

(x+y+z-xyz)/(1-xy-xz+yz)
i don't know how to simplify it to reach xy+yz+zx

Answer 2

i think there ia an error in denominator, u should get 1-xy-xz-yx
then since arctan(..../....) is pi/2, u get (..../...) = infinity.
that means denominator =0
1-xy-xz-yx=0
and u are done....
so just check your denominator

Answer 3

ok thanks

Answer 4

sorry, i meant 1-xy-zx-yz=0

Answer 5

so do i move that to the right hand side

Answer 6

1-xy-zx-yz=0
1=xy+zx+yz
if u meant ^ then,yes.