" If "2cos theta-sin theta=x" and "cos theta-3sin theta=y." Prove that "2x^(2)+y^(2)-2xy=5" ."

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 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 x sin^(3)theta+y cos^(3)theta=sin theta cos theta andx sin theta=y cos theta prove that x^(2)+y^(2)=1

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 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 :x^(2)+y^(2)=a^(2)+b^(2)

If xsin^(3) theta +y cos^(3) theta=sin theta cos theta and x sin theta =y cos theta , then prove that x^(2)+y^(2)=1 .

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