InterviewSolution
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InterviewSolution
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If ` x=r sin alpha cos beta, y= r sin alpha sin beta and z= r cos alpha , ` prove that ` x^(2)+y^(2) + z^(2) = r^(2). ` |
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Answer» We have ` x^(2) + y^(2) + z^(2) = r^(2) sin^(2) alpha cos^(2) beta +r^(2) sin^(2) alpha sin^(2) beta + r^(2) cos^(2) alpha ` ` = r^(2)sin^(2) alpha (cos^(2) beta + sin^(2) beta) + r^(2) cos^(2) alpha ` `= r^(2) sin^(2) alpha + r^(2) cos^(2) alpha " " [because cos^(2) beta + sin^(2) beta =1] ` `= r^(2) (sin^(2) alpha + cos^(2) alpha )= r^(2) " " [because sin^(2) alpha + cos^(2) alpha =1]. ` Hence, ` (x^(2) + y^(2) + z^(2))= r^(2) . ` |
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