If x = r cos theta cos phi,y = r cos theta si | vedclass

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(A) Given:$x = r \cos 	heta \cos \phi$$y = r \cos 	heta \sin \phi$$z = r \sin 	heta$Substituting these into the expression $x^{2} + y^{2} + z^{2}$:

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$r^{2}$

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(A) Given:$x = r \cos 	heta \cos \phi$$y = r \cos 	heta \sin \phi$$z = r \sin 	heta$Substituting these into the expression $x^{2} + y^{2} + z^{2}$:$x^{2} + y^{2} + z^{2} = (r \cos 	heta \cos \phi)^{2} + (r \cos 	heta \sin \phi)^{2} + (r \sin 	heta)^{2}$$= r^{2} \cos^{2} 	heta \cos^{2} \phi + r^{2} \cos^{2} 	heta \sin^{2} \phi + r^{2} \sin^{2} 	heta$Factoring out $r^{2} \cos^{2} 	heta$ from the first two terms:$= r^{2} \cos^{2} 	heta (\cos^{2} \phi + \sin^{2} \phi) + r^{2} \sin^{2} 	heta$Since $\cos^{2} \phi + \sin^{2} \phi = 1$:$= r^{2} \cos^{2} 	heta (1) + r^{2} \sin^{2} 	heta$$= r^{2} (\cos^{2} 	heta + \sin^{2} 	heta)$Since $\cos^{2} 	heta + \sin^{2} 	heta = 1$:$= r^{2} (1) = r^{2}$

If $x = r \cos \theta \cos \phi$,$y = r \cos \theta \sin \phi$,and $z = r \sin \theta$,then the value of $x^{2} + y^{2} + z^{2}$ is

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