Question

if x = r sin thita cos thita , y= r= sin thita sin thita z= r cos thita . prove that x square+y square+ z square = r square​

Answer 1

Correct Question:-

If x = r * Sin A * Cos π ; y = r * Sin A * Sin π ; z = r * Cos A then prove that x² + y² + z² = r²

Answer:-

Given:

x = r * Sin A * Cos 180°

x = - r * Sin A

y = r * Sin A * Sin 180°

y = 0

z = r * Cos A

x² + y² + z² = r²

Putting the values,

( r * - Sin A )² + 0² + (r * Cos A)² = r²

r² Sin² A + r² Cos² A = r²

r²(Sin² A + Cos² A) = r²

r²(1) = r²

r² = r²

LHS = RHS.

Hence, proved.