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

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

If (x)/(a) cos theta + (y)/(b) sin theta = 1 , (x)/(a) sin theta - (y)/(b) cos theta =1 then

If x=a cos theta + b sin theta and y=a sin theta - b cos theta. then a ^(2) +b^(2) is equal to

If x=a cos theta + b sin theta and y=a sin theta - b cos theta. then a ^(2) +b^(2) is equal to

If a sin^(3) theta + b cos^(3) theta = sin^(3) theta * cos theta and a sin theta - b cos theta=0 , then prove that a^(2)+b^(2)=1 .

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