X=r sin alpha cos beta,y=r sin alpha sin beta,z=r cos alpha to provex^2+y^2+z^2=r^2 Share with your friends Share 0 Varun.Rawat answered this We have,x = r sin α . cos βy = r sin α . sin βz = r cos αNow, LHS = x2+y2+z2=r sin α . cos β2 + r sin α . sin β2 + r cos α2=r2 sin2α . cos2β + r2sin2α . sin2β + r2cos2α=r2 sin2αcos2β + sin2β + r2cos2α=r2 sin2α × 1× + r2cos2α=r2 sin2α + r2cos2α=r2sin2α + cos2α=r2×1=r2=RHS 0 View Full Answer Archit Anand K.p. answered this LHS=X^2+y^2+z^2 RHS=r^2 =r^2 sin^2α cos^β + r^2 sin^2α sin^2β + r^2 cos^α =r^2 sin^2α (cos^2β + sin^2β) +r^2 cos^α (sin^2ᶱ + cos^2ᶱ = 1) =r^2 sinα+r^2 cosα =r^2 (sin^2α+cos^2α) (sin^2ᶱ + cos^2ᶱ = 1) =r^2=RHS 0
