If x = r sin $\theta$ cos ϕ, y = r sin $\theta$ sin ϕ and z = r cos $\theta$, then

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Given: x= r sin $\theta$ cos Φ, y=r sin$\theta$ sinΦ z= r cos $\theta$ Squaring and adding these equations, we get `x^2+y^2+z^2=(r sin$\theta$ cosΦ )^2+(r sin $\theta$ sinΦ )^2+(r cos $\theta$)^2 = x^2+y^2+z^2=r^2 sin^2$\theta$ cos^2Φ+r^2 sin^2$\theta$sin^2Φ+r^2 cos^2$\theta$ =x^2+y^2+z^2=(r^2 sin^2$\theta$ cos^2Φ+r^2 sin^2 sin^2Φ)+r^2 cos^2Φ =x^2+y^2+z^2=r^2sin^2$\theta$(cos^2Φ+sin^2Φ)+r^2 cos^2Φ =x^2+y^2+z^2=r^2 sin^2$\theta$(1)+r^2 cos^2$\theta$ =x^2+y^2+z^2=r^2 sin^2$\theta$+r^2 cos^2$\theta$ =x^2+y^2+z^2=r^2(sin^2$\theta$+cos^2$\theta$) =x^2+y^2+z^2=r^2(1) =x^2+y^2+z^2=r^2`

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