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Question
If x = r sinA cosB , y = r sinA sinB and z = r cosA , prove that `x^2 + y^2 + z^2 = r^2`
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Solution
LHS = `(rsinAcosB)^2 + (rsinAsinB)^2 + (rcosA)^2`
⇒ `r^2sin^2Acos^2B + r^2sin^2Asin^2B + r^2cos^2A`
⇒ `r^2sin^2A(cos^2B + sin^2B) + r^2cos^2A`
⇒ `r^2(sin^2A + cos^2A) = r^2` = RHS
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