Let `0 lt=thetalt=pi/2 and x=X cos theta+Y sin theta, y=X sin theta-Y cos theta` such that `x^2+2xy+y^2=aX^2+bY^2,` where a and b are constant, then

Let 0 leq theta leq (pi)/(2) and x=X cos theta+Y sin theta y=X sin theta-Y cos theta such that x^(2)+4 x y+y^(2)=a X^(2)+b Y^(2) where a, b are constants, then

Let 0<=theta<=(pi)/(2)x=X cos theta+Y sin thetay=X sin theta-Y cos theta such that x^(2)+4xy+y^(2)=aX^(2)+bY^(2) where a,b are constants such that

If x cos 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, 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 = X cos theta- Y sin theta, y = X sin theta + Y cos theta and x^2 + 4 x y + y^2 = A X^2 + B Y^2 0 <= theta <= pi/2, then

If x=X cos theta- Y sin theta, y= X sin theta+ Y cos theta and x^(2)+4xy+y^(2)=AX^(2), B^(2),"for " 0 le theta le (pi)/(2) then (A,B)=

x=a sin theta, y=a cos theta " then "x^2+y^2 =…………