Question

If x =r sinA cos C, y= r sin A sin C, z=rcos A, Prove that r 2 = x 2 +y 2 +z 2

Answer 1

 r^2 = x^2 +y^2 +z^2
R.H.S= x^2 +y^2 +z^2
          =r^sin^2(a)cos^2(c) + r^2sin^2(a)sin^2(c) + r^2cos^2(A)
         = r^2[ sin^2(a)cos^2(c) + sin^2(a)sin^2(c) +cos^2(a) ]
         =r^2[ sin^2(a)[cos^2(c) +sin^2(c)] +cos^2(a) ]
         =r^2{ sin^(a)[ 1 ] + cos^2(a) }
         =r^2{ sin^2(a) +cos^2(a)}
        =r^2 {1  } 
        =r^2//