If xyz=1 then show that `(1+x+y^-1)^-1+(1+y+z^-1)^-1+(1+z+x^-1)^-1=1 `

If x+y+z=a , show that (1/x+1/y+1/z)^-1ge9/a

If cos^(-1)x + cos^(-1)y - cos^(-1) z = 0 , then show that x^(2) + y^(2) + z^(2) - 2xyz = 1

If x + y + z = xyz , prove that x(1 -y^(2)) (1- z^(2))+ y(1- z^(2))(1- x^(2)) +z(1-x^(2)) (1- y^(2)) = 4xyz .

If xy + yz + zx = 1 , show that x/(1-x^(2)) +y/(1-y^(2)) + z/(1-z^(2))= (4xyz)/((1-x^(2))(1-y^(2)) (1-z^(2)))

If xy + yz + zx = 1 , show that x/(1-x^(2)) +y/(1-y^(2)) + z/(1-z^(2))= 4xyz/((1-x^(2))(1-y^(2)) (1-z^(2)))

If xyz = 1, then find the value of 1/((1+x+y^(-1)))+1/((1+y+z^(-1)))+1/((1+z+x^(-1))) .

If x+y+z=xyz then show that (2x)/(1-x^(2))+(2y)/(1-y^(2))+(2z)/(1-z^(2))=(8xyz)/((1-x^(2))(1-y^(2))(1-z^(2)))

If x+y+z=xyz , then tan^(-1)x+tan^(-1)y+tan^(-1)z=

If x+y+z=xyz , then tan^(-1)x+tan^(-1)y+tan^(-1)z=