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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

Posted by Chetan ._. 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Since, x² = r²sin²Acos²B
y ² = r²sin²A sin²B
and z² = r²cos²A
L.H.S. = x² + y² + z²
{tex}=r^2sin^2Acos^2B+r^2sin^2Asin^2B+r^2cos^2A{/tex}
= {tex}r^2sin^2A(cos^2B+sin^2B)+r^2cos^2A{/tex}
= r²sin² A + r²cos²A
= r²(sin² A + cos²A)
= r².
= R.H.S
Hence Proved.

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CBSE > Class 10 > Mathematics