If x = 3 sin theta,y = 3 cos theta cos phi,an | vedclass

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(C) Given: $x = 3 \sin 	heta$,$y = 3 \cos 	heta \cos \phi$,$z = 3 \cos 	heta \sin \phi$ $x^{2} + y^{2} + z^{2} = (3 \sin 	heta)^{2} + (3 \cos 	he

Vedclass · Accepted Answer

$9$

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(C) Given: $x = 3 \sin 	heta$,$y = 3 \cos 	heta \cos \phi$,$z = 3 \cos 	heta \sin \phi$ $x^{2} + y^{2} + z^{2} = (3 \sin 	heta)^{2} + (3 \cos 	heta \cos \phi)^{2} + (3 \cos 	heta \sin \phi)^{2}$ $= 9 \sin^{2} 	heta + 9 \cos^{2} 	heta \cos^{2} \phi + 9 \cos^{2} 	heta \sin^{2} \phi$ $= 9 \sin^{2} 	heta + 9 \cos^{2} 	heta (\cos^{2} \phi + \sin^{2} \phi)$ Since $\cos^{2} \phi + \sin^{2} \phi = 1$: $= 9 \sin^{2} 	heta + 9 \cos^{2} 	heta (1)$ $= 9 (\sin^{2} 	heta + \cos^{2} 	heta)$ Since $\sin^{2} 	heta + \cos^{2} 	heta = 1$: $= 9 	imes 1 = 9$

If $x = 3 \sin \theta$,$y = 3 \cos \theta \cos \phi$,and $z = 3 \cos \theta \sin \phi$,then $x^{2} + y^{2} + z^{2} =$

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