[" 32.If "2cos theta-sin theta=x" and "cos theta-3sin theta=y],[" Prove that ":2x^(2)+y^(2)-2xy=5],[" Or "]

If x=cosec theta-sin theta and y=sec theta-cos theta then prove that x^(2/3)+y^(2/3)=(xy)^(-2/3)

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

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 =2cos theta-cos2 theta and y=2sin theta-sin2 theta Prove that (dy)/(dx)=tan((3 theta)/(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 = 3 sin theta + 4 cos theta and y = 3 cos theta - 4 sin theta then prove that x^(2) + y^(2) = 25 .

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 = 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