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-1x+tan-1y+tan-1z = π/2 =) tan-1x+tan-1y = π/2-tan-1z =) tan(tan-1x+tan-1y) = tan(π/2-tan-1z) = ) x+y/1-xy = cot(tan-1z) [since tan(A+B)=tanA+tanB/1-tanAtanB & tan(π/2-A)=cotA] =) x+y/1-xy = cot(cot-11/z) [since tan-1A=cot-11/A] = ) x+y/1-xy = 1/z =) xz+yz=1-xy [by cross multiplication] =) xy+yz+zx=1 AS DESIRED // 70
