If $x=r\cos \alpha \cos \beta \cos \gamma ,y=r\cos \alpha \cos \beta \sin \gamma ,z=r\sin \alpha \cos \beta$,  and $\mu =r\sin \beta$, then  $x^2+y^2+z^2+{\mu }^2=$

$x=r\cos \alpha \cos \beta \cos \gamma$

$y=r\cos \alpha \cos \beta \sin \gamma$

$z=r\sin \alpha \cos \beta$

$u=r\sin \beta$

$x^2+y^2+z^2+{\mu }^2$

$=r^2{\cos }^2\alpha {\cos }^2\beta {\cos }^2\gamma +r^2{\cos }^2\alpha {\cos }^2\beta {\sin }^2\gamma +r^2{\sin }^2\alpha {\cos }^2\beta +r^2{\sin }^2\beta$

$=r^2{\cos }^2\alpha {\cos }^2\beta ({\cos }^2\gamma +{\sin }^2\gamma )+r^2{\sin }^2\alpha {\cos }^2\beta +r^2{\sin }^2\beta$

$=r^2{\cos }^2\alpha {\cos }^2\beta +r^2{\sin }^2\alpha {\cos }^2\beta +r^2{\sin }^2\beta$

$=r^2{\cos }^2\beta ({\cos }^2\alpha +{\sin }^2\alpha )+r^2{\sin }^2\beta$

$=r^2{\cos }^2\beta +r^2{\sin }^2\beta$

$=r^2\left(1\right)=r^2$