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

If x sin^3 theta+ y cos^3 theta = sin theta cos theta and x sin theta = y cos theta, Find the value of x^2 + y^2.

Prove that sin^6theta+cos^6theta=1-3sin^2thetacos^2theta

If x=a(costheta+thetasintheta) , y=a(sintheta-thetacostheta) , prove that (d^2x)/(d theta^2)=a(costheta-thetasintheta) , (d^2y)/(d theta^(2))=a(sintheta+thetacostheta) and (d^2y)/(dx^2)=(s e c^3theta)/(a\ theta)

If acos^3theta+3acosthetasin^2theta=m and asin^3theta+3acos^2thetasintheta=n , then prove that: (m+n)^(2//3)+(m-n)^(2//3)=2a^(2//3)

The equation of the straight line passing through the point (acos^3theta,asin^3theta) and perpendicular to the line xsectheta+ycos e ctheta=a is (A) xcostheta-ysintheta=acos2theta (B) xcostheta+ysintheta=acos2theta (C) xsintheta+ycostheta=acos2theta (D) none of these

If acos^3theta+3acosthetasin^2theta=m and asin^3theta+3acos^2thetasin^theta=n , then prove that: (m+n)^(2//3)+(m-n)^(2//3)=2a^(2//3)

Prove that cos^6 theta+ sin^6 theta= 1-3sin^2 theta cos^2 theta

Prove that : cos^3 2theta+3cos2theta=4(cos^6theta-sin^6 theta)

If xsin(90^@-theta)cot(90^@-theta)=cos(90^@-theta) , then x=

If x = 2 cos theta - cos 2theta and y = 2 sin theta - sin 2theta then prove that : (dy)/(dx)=tan (3 theta)/(2)