It is given that \(z=x\)

(a) In the cylindrical coordinates, \(z=z,x=r\cos\theta\)

Hence the equation becomes, \(z=r\sin\theta\)

(b) In the spherical coordinates, \(x=\rho\sin\theta\cos\phi;z=\rho\cos\theta\)

Hence the equation becomes \(\rho\cos\theta=\rho\sin\theta\cos\phi\)

After rearranging the terms, \(\cot\theta=\cos\phi\)