Question

X=r cosa sinb y =r cos a cos b and z=r sin a then prove that x2+y2+z2=r2

Answer 1

Step-by-step explanation:

x = r sinA cosC, y = r sinA sinC, z = r cosA

x2 + y2 + z2 = r2 sin2A cos2C + r2 sin2A sin2C + r2 cos2A

= r2 sin2A (cos2C + sin2C) + r2 cos2A

= r2sin2A + r2cos2A

= r2(sin2A + cos2A)

= r2 (since, sin2+ cos2 = 1)