[ using identity cosec ^(2)A=1+cot^(2)A 4.If x sin^(3)|+y cos^(3)|=sin|cos| and xsin |= ycos |, prove x^(2)+y^(2)=1]

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 xsin^3theta+ycos^3theta=sinthetacostheta and xsintheta=ycostheta, prove that x^2+y^2=1

If xsin^3a+ycos^3a = sin a cos a and x sin a- y cos a = 0 , then show that x^2+y^2= 1 .

If xsin^3theta+ycos^3theta=sinthetacosthetaa n dxsintheta=ycostheta, prove that x^2+y^2=1

if xsin^3theta+ycos^3theta =sin theta cos theta and x sin theta -y cos theta =0 prove that x^2+y^2=1

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 2y cos theta =x sin theta and 2x sec theta -y cosec theta =3, then x ^(2) +4y^(2)=

Consider the system of equations x cos ^(3) y + 3 x cosy sin^(2) y = 14 t o (1) and x sin^(3) y + 3 x cos^(2) y sin y = 13 to (2) The value of sin^(2) y + 2 cos^(2) y is

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