If `2^x = 3^y =12^z` show that `1/z= 1/y+2/x`

If 2^(x)=3^(y)=12^(z) show that xy=z(x+2y)

If cos^-1 x +cos^-1y + cos^-1z = pi and x + y + z = 3/2 , then show that x = y = z.

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 x + y + z =xyz,show that (2x)/(1-x^2)+(2y)/(1-y^2)+(2z)/(1-z^2)=(2x)/(1-x^2).(2y)/(1-y^2).(2z)/(1-z^2)

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 x+y+z=xyz , show that : (3x-x^3)/(1-3x^2) + (3y-y^3)/(1-3y^2) + (3z-z^3)/(1-3z^2) = (3x-x^3)/(1-3x^2) . (3y-y^3)/(1-3y^2) . (3z-z^3)/(1-3z^2)

If z= x + yi and |2z + 1| = |z- 2i| , show that 3(x^(2) + y^(2)) + 4(x-y)=3

If z = x + iy and |2z+1|=|z-2i| ,then show that 3(x^(2)+y^(2))+4(x+y)=3

If x,y,z are different and Delta = |(x, x^2, 1+x^3),(y,y^2,1+y^3),(z,z^2,1+z^3)|= 0 then show that 1 + xyz = 0