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

Question

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

Aicharya · Accepted Answer

$\begin{aligned} x^{2}+y^{2}+z^{2} &=9 \sin ^{2} 	heta+9 \cos ^{2} 	heta \cos ^{2} \phi+9 \cos ^{2} 	heta \sin ^{2} \phi \ &=9 \sin ^{2} 	heta+9 \cos ^{2} 	heta\left(\cos ^{2} \phi+\sin ^{2} \phiight) \ &=9 \sin ^{2} 	heta+9 \cos ^{2} 	heta \ &=9\left(\sin ^{2} 	heta+\cos ^{2} 	hetaight)=9 	imes 1=9 \end{aligned}$

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

Solution