Question

if x=sinAcosC, by=rsinAsinC, z= rcosA then prove that x^y^z^=r^ in a easy way​

Answer 1

x=rsinAcosC⇒x2=r2sin2Acos2C

y=rsinAsinC⇒y2=r2sin2Asin2C

z=rcosA⇒r2cos2A

To Prove:- x2+y2+z2=r2

Proof:-

Taking L.H.S.-

x2+y2+z2

=r2sin2Acos2C+r2sin2Asin2C+r2cos2A

=r2sin2A(cos2C+sin2C)+r2cos2A

=r2sin2A+r