[" 30) "hat y tan(yz)/(xz)+tan^(7)(zx)/(yz)+tan^(-1)(xy)/(zz)=(pi)/(2)" if "],[" Airctia "sin(1)/(2)x^(2)+y^(2)+z^(2)=z^(2)],[" (oq) "]

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)

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

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)

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 .

Prove the followings : If tan^(-1)((yz)/(xr))+tan^(-1)((zx)/(yr))+tan^(-1)((xy)/(zr))=pi/2 then x^(2)+y^(2)+z^(2)=r^(2) .

(x-y-z)^(2)-(x^(2)+y^(2)+z^(2))=2(yz-zx-xy)

" (a) "tan^(-1)x+tan^(-1)y+tan^(-1)z=tan^(-1)(x+y+z-xyz)/(1-xy-yz-zx)

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

tan^(-1)""(x-y)/(1+xy)+tan^(-1)""(y-z)/(1+yz)+tan^(-1)""(z-x)/(1+zx) =tan^(-1)""(x^(2)-y^(2))/(1+x^(2)y^(2))+tan^(-1)""(y^(2)-z^(2))/(1+y^(2)z^(2))+tan^(-1) ""(z^(2)-x^(2))/(1+z^(2)x^(2))

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