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If $x=3 \sin \theta, y=3 \cos \theta \cos \phi, z=3 \cos \theta \sin \emptyset$, then $x^{2}+y^{2}+z^{2}=$
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The correct answer is:
$9$
$\begin{aligned} x^{2}+y^{2}+z^{2} &=9 \sin ^{2} \theta+9 \cos ^{2} \theta \cos ^{2} \phi+9 \cos ^{2} \theta \sin ^{2} \phi \\ &=9 \sin ^{2} \theta+9 \cos ^{2} \theta\left(\cos ^{2} \phi+\sin ^{2} \phi\right) \\ &=9 \sin ^{2} \theta+9 \cos ^{2} \theta \\ &=9\left(\sin ^{2} \theta+\cos ^{2} \theta\right)=9 \times 1=9 \end{aligned}$
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