If x = r sinAcosB,  y = r sinAcosB and z= r cosA, show that x² + y²+ z²= r².

Asked by pdcavita | 18th Nov, 2017, 12:46: PM

Expert Answer:

begin mathsize 16px style space straight x equals straight r space sin space straight A space cos space straight B comma space space straight y equals straight r space sin space straight A space sin space straight B space and space straight z equals straight r space cos space straight A
straight x squared plus straight y squared plus straight z squared
equals straight r squared space sin squared space straight A space cos to the power of space 2 end exponent space straight B plus straight r squared space sin squared space straight A space sin squared space straight B plus straight r squared space cos squared space straight A
equals straight r squared sin squared space straight A space left parenthesis cos to the power of space 2 end exponent space straight B plus sin squared space straight B right parenthesis plus straight r squared space cos squared space straight A
equals straight r squared sin squared space straight A plus straight r squared space cos squared space straight A
equals straight r squared left parenthesis sin squared space straight A plus cos squared space straight A right parenthesis
equals straight r squared
end style

Answered by Rashmi Khot | 5th Dec, 2017, 04:00: PM