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Question

If x=rsinAsinB,y=rcosAsinB,z=rcosB, then x2+y2+z2 is equal to

A
2r2
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B
r2
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C
3r2
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D
r2+1
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Solution

The correct option is B r2
x2+y2+z2
=r2sin2Asin2B+r2cos2Asin2B+r2cos2B
=r2sin2B(sin2A+cos2A)+r2cos2B
=r2sin2B+r2cos2B
=r2(sin2B+cos2B)
=r2

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