If x = r `cos theta and y =r sin theta`, then proof `x^2 + y^2 = r^2 `

Solve the following: If x = r cos theta and y = r sin theta , then prove x^2 + y^2 = r^2

If x=r cos theta,y=r sin theta, show that

If x = r cos theta cos phi, y = r cos theta sin phiz = r sin theta, then x ^ (2) + y ^ (2) + z ^ (2) = (i) r ^ (2) (ii ) y ^ (2) (iii) x ^ (2) (iv) z ^ (2)

If x = r cos theta and y = r sin theta, prove that (del ^ (2) r) / (del x ^ (2)) + (del ^ (2) r) / (del y ^ (2)) = (1) / (r) [((del r) / (del x)) ^ (2) + ((del r) / (del y)) ^ (2)]

If x = r cos theta, y = r sin theta then prove that (del (x, y)) / (del (r, theta)) xx (del (r, theta)) / (del (x, y)) = 1

Find dy/dx : x = r cos theta, y = r sin theta

If x = 3 sin theta + 4 cos theta and y = 3 cos theta - 4 sin theta then prove that x^(2) + y^(2) = 25 .

If x = 3sin theta + 4cos theta and y = 3cos theta - 4 sin theta then prove that x^(2) + y^(2) = 25 .

If x = rsin theta*cos phi , y = rsin theta*sin phi and z = rcos theta then prove that x^2 + y^2 + z^2 = r^2

If x = a cos theta - b sin theta and y = a sin theta + b cos theta, prove that x^2 + y^2 = a^2 + b^2.