If x=rsinAcosB,y=rsinAsinB andz=rcosA, then prove that r sq=x sq+y sq+

1.	If x=rsinAcosB,y=rsinAsinB andz=rcosA, then prove that r sq=x sq+y sq+z sq
Answer» Since, x2 = r2sin2Acos2By 2 = r2sin2A sin2Band z2 = r2cos2AL.H.S. = x2 + y2 + z2{tex}=r^2sin^2Acos^2B+r^2sin^2Asin^2B+r^2cos^2A{/tex}=\xa0{tex}r^2sin^2A(cos^2B+sin^2B)+r^2cos^2A{/tex}= r2sin2 A + r2cos2A= r2(sin2 A + cos2A)= r2.= R.H.SHence Proved.

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