IF `tan ^(-1) x + tan ^(-1) y + tan ^(-1) ""z=(pi)/(2) , x+y+z=sqrt(3)` , prove that ` x=y=z`

If tan ^(-1) ""x + tan ^(-1) ""y + tan ^(-1) ""z=(pi)/(2) and x + y +z = sqrt(3) then show that x =y=z.

if tan ^(-1) x+tan ^(-1)y+tan ^(-1) z=pi/2 and x+y+z= sqrt3 , then show that x=y=z.

if tan ^(-1) x+tan ^(-1) y+tan ^(-1) z=pi prove that x+y+z=xyz

"If " tan^(-1) x+ tan^(-1) y+tan ^(-1)z=(pi)/(2) , show that , xy+yz+zx =1

If tan ^(-1 )""(yz )/( xr ) + tan ^(-1 )""(zx)/(yr) + tan ^(-1) ""(xy)/(zr) =(pi)/(2) , prove that , x^(2) + y^(2) + z^(2) + r^(2)

Let tan ^(-1) y= tan ^(-1) x+ tan ^(-1) ""((2x)/(1-x^(2))) where |x| lt (1)/(sqrt(3)) . Then a value of y is -

If tan^(-1) [(yz)/(xr)] + tan^(-1) [(zx)/(yr)]+ tan^(-1) [(xy)/(zr)] = pi /2 prove that, x^2 + y^2 + z^2 = r^2 .

tan ^(-1)x-tan ^(-1)y=sin ^(-1) ""(x-y)/(sqrt((1+x^(2))(1+y^(2)))

IF sin ^(-1)x + sin ^(-1) y+ sin ^(-1)""z=(3pi)/(2), then the value of x^(9) +y^(9) +z^(9)-""(1)/(x^(9)y^(-9)z^(9)) is equal to -

If tan^(-1)x+tan^(-1)y+tan^(-1)z=pi/2,t h e n x+y+z-x y z=0 x+y+z+x y z=0 x y+y z+z x+1=0 x y+y z+z x-1=0