`tan^(- 1)(sqrt(x(x+y+z))/(y z))+tan^(- 1)sqrt((y(x+y+z))/(xz))+tan^(- 1)(sqrt((z(x+y+z))/(x y)))=pi`

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))

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))

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

Tan ^ (- 1) (yz) / (x sqrt (x ^ (2) + y ^ (2) + z ^ (2))) + (tan ^ (- 1) (zx)) / (y sqrt ( x ^ (2) + y ^ (2) + z ^ (2))) + (tan ^ (- 1) (xy)) / (z sqrt (x ^ (2) + y ^ (2) + z ^ (2)))

If x, y, z are all non zero and x^(2)+y^(2)+z^(2)=r^(2) then tan ^(-1)((y z)/(x r))+tan ^(-1)((z x)/(y r))+tan ^(-1)((x y)/(z r))

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))

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

If x, y, z are in A.P then 1/(sqrt(x) + sqrt(y)) , 1/(sqrt(z) + sqrt(x)) , 1/(sqrt(y) + sqrt(z)) are in

If the number x,y,z are in H.P.,then (sqrt(yz))/(sqrt(y)+sqrt(z)),(sqrt(xz))/(sqrt(x)+sqrt(z)),(sqrt(x))/(sqrt(x)+sqrt(y)) are in