Question

If x =r cos A sin B, y = r cos A cosB and z =r sinA, then prove that x² + y^2+z^2 = r^2​

Answer 1

Answer:

which standard you are in

Answer 2

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

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

² cos²A

= r² sin²A (cos²C + sin²C) + r² cos²A

= r²sin²A + r²cos²A

= r²(sin²A + cos²A)

= r² (since, sin²e + cos²e = 1)