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If x=rsinAcosB,y=rsinAsinB andz=rcosA, then prove that …

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If x=rsinAcosB,y=rsinAsinB andz=rcosA, then prove that r sq=x sq+y sq+z sq
  • 1 answers

Sia ? 6 years ago

Since, x2 = r2sin2Acos2B
y 2 = r2sin2A sin2B
and z2 = r2cos2A
L.H.S. = x2 + y2 + z2
=r2sin2Acos2B+r2sin2Asin2B+r2cos2A
r2sin2A(cos2B+sin2B)+r2cos2A
= r2sin2 A + r2cos2A
= r2(sin2 A + cos2A)
= r2.
= R.H.S
Hence Proved.

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