Taking LHS = x2 + y2 + z2
Putting the values of x, y and z , we get
=(r cos α sin β)2 + (r sin α sin β)2 + (r cos α)2
= r2 cos2α sin2β + r2 sin2α sin2β + r2 cos2α
Taking common r2 sin2 α , we get
= r2 sin2α (cos2β + sin2 β) + r2cos2 α
= r2 sin2α + r2 cos2 α [∵ cos2 β + sin2 β = 1]
=r2 ( sin2 α + cos2 α)
= r2 [∵ cos2 α + sin2 α = 1]
= RHS
Hence Proved