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

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

If a cos theta+b sin theta=m and a sin theta-b cos theta=n, prove that a^(2)+b^(2)=m^(2)+n^(2)

If a cos theta+b sin theta=m and a sin theta-b cos theta=n, Prove that a^(2)+b^(2)=m^(2)+n^(2)

If x=a sin theta+b cos theta,y=a cos theta-b sin theta then show that (ax+by)^(2)+(bx-ay)^(2)=(a^(2)+b^(2))^(2)

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

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

If a cos theta+bs int h eta=x and a sin theta-b cos theta=y, prove that a^(2)+b^(2)=x^(2)+y^(2)