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`cot^(-1)((xy+1)/(x-y)) + cot^(-1)((yz+1)/(y-z))+ cot^(-1) ((zx+1)/(z-x)) = 0(0lt xy,yz, zx lt 1)`

Prove that following cot^(-1)((xy+1)/(x-y)) +cot^(-1)((yz+1)/(y-z))+cot^(-1)((zx+1)/(z-x))=0, (0 lt xy, yz, zx lt 1)

If x>y>z>0, then find the value of cot^(-1)(xy+1)/(x-y)+cot^(-1)(yz+1)/(zy-z)+cot^(-1)(zx+1)/(z-x)

If x gt y gt z gt 0 , then find the value of "cot"^(-1) (xy + 1)/(x - y) + cot^(-1).(yz + 1)/(y - z) + cot^(-1).(zx + 1)/(z - x)

If x gt y gt z gt 0 , then find the value of "cot"^(-1) (xy + 1)/(x - y) + "cot"^(-1)(yz + 1)/(y - z) + "cot"^(-1)(zx + 1)/(z - x)

If cot^(-1)x + cot^(-1)y + cot^(-1)z = pi , prove that xy + yz + zx = 1 .

If cos^(-1)x + cos^(-1)y + cos^(-1)z = pi, then xy + yz +zx is equal to

If cos^(-1)x + cos^(-1)y + cos^(-1)z = pi, then xy + yz +zx is equal to

tan^(-1) x + tan^(-1) y + tan^(-1) z = (pi)/2 show that : xy + yz + zx = 1 .