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If x=rsinAcosC , y=rsinAsinC and z=rcosA prove that r^2=x^2+y^2+z^2

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Solution: We have ,

$\ x^2+y^2+z^2=r^2sin^2Acos^2C+r^2sin^2Asin^2C+r^2cos^2A\ \Rightarrow x^2+y^2+z^2=r^2sin^2A(cos^2C+sin^2C)+r^2cos^2A\ \Rightarrow x^2+y^2+z^2=r^2sin^2A+r^2cos^2A=r^2$

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Deependra Verma

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