[" If "x=a sin theta+b cos thetaquad " and "quad y=a cos theta-b sin theta,quad " prove "quad " that "],[x^(2)+y^(2)=a^(2)+b^(2)]

x = a cos theta, y = b sin theta .

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

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 = sin theta + cos theta sin 2 theta " and " y = cos theta + sin theta sin 2 theta,"prove that " (x+y)^(2//3) + (x-y)^(2//3) = 2

If x=2 cos theta- cos 2 theta and y=2 sin theta - sin 2 theta, then (dy)/(dx) =

If x=2 cos theta- cos 2 theta and y=2 sin theta - sin 2 theta, then (dy)/(dx) =

If x=a cos theta-b sin theta and y=a sin theta+b cos theta then prove that :x^(2)+y^(2)=a^(2)+b^(2)

If xcos theta- y sin theta =a, x sin theta + y cos theta = b , prove that: x^(2) + y^(2) = a^(2) + b^(2) .

If x=a cos theta+b sin theta and y=a sin theta-b cos theta, then prove that y^(2)(d^(2)y)/(dx^(2))-x(dy)/(dx)+y=0