Question

If x=rsinθcosϕ,y=rsinθsinϕandz =rcosθ, then x2+y2+z2=​

Answer 1

now we taken

theta =a,pai=b

x=rsin(a)cos(b),y=rsin(a)sin(b),z=rcos(a)

=x2+y2+z2

=r2sin2 (a) cos2 (b)+r2sin2 (a)+sin2sin (b)+r2cos2 (a)

=r2sin2 (a){cos2 (b)+sin2 (b)}+r2cos2 (a)

=r2sin2 (a)+r2cos2 (a)【since sin2 (b)+cos2(b)=1】

=r2{sin2 (a)+cos2 (a)}

=r2

x2+y2+z2=r2