$I f x = r \cos α \cos β \cos γ; y = r \cos α \cos β \sin γ; z = r \sin α \cos β, μ = r \sin β t h e n x^{2} + y^{2} + z^{2} + μ^{2} =$

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$r^{2}$

$4 r^{2}$

answer is C.

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Detailed Solution

$x = r \cos α \cos β \cos γ y = r \cos α \cos β \sin γ z = r \sin α \cos β μ = r \sin β$

$\begin{array}{rcl} x^{2} + y^{2} + z^{2} + μ^{2} \\ = & r^{2} \cos^{2} α \cos^{2} β \cos^{2} γ + r^{2} \cos^{2} α \cos^{2} β \sin^{2} γ \\ + r^{2} \sin^{2} α \cos^{2} β + r^{2} \sin^{2} β \\ = & r^{2} \cos^{2} α \cos^{2} β (\cos^{2} γ + \sin^{2} γ) + r^{2} \sin^{2} α \cos^{2} β + r^{2} \sin^{2} β \\ = & r^{2} \cos^{2} α \cos^{2} β + r^{2} + \sin^{2} α \cos^{2} β + r^{2} \sin^{2} β \\ = & r^{2} \cos^{2} β (\cos^{2} α + \sin^{2} α) + r^{2} \sin^{2} β \\ = & r^{2} \cos^{2} β + r^{2} \sin^{2} β \\ = & r^{2} (\cos^{2} β + \sin^{2} β) \\ = & r^{2} \end{array}$