if tan-1x+tan-1y+tan-1z=π/2 show that xy+yz+zx=1? Share with your friends Share 34 Pooja Khanna answered this Here is the link for the answer to your query: https://www.meritnation.com/ask-answer/question/tan-1-x-tan-1-y-tan-1-z-pi-2-show-that-xy-yz-zx-1/math/9302317 7 View Full Answer Sachin Dravid answered this tan^{-1}x+tan^{-1}y+tan^{-1}z = π/2 =) tan^{-1}x+tan^{-1}y = π/2-tan^{-1}z =) tan(tan^{-1}x+tan^{-1}y) = tan(π/2-tan^{-1}z) = ) x+y/1-xy = cot(tan^{-1}z) [since tan(A+B)=tanA+tanB/1-tanAtanB & tan(π/2-A)=cotA] =) x+y/1-xy = cot(cot^{-1}1/z) [since tan^{-1}A=cot^{-1}1/A] = ) x+y/1-xy = 1/z =) xz+yz=1-xy [by cross multiplication] =) xy+yz+zx=1 AS DESIRED _{//} 70