If `x=a(1-costheta)` , `y=a(theta+sintheta)` , prove that `(d^2y)/(dx^2)=-1/a` at `theta=pi/2` .

If x=a(1-cos theta),y=a(theta+sin theta), prove that (d^(2)y)/(dx^(2))=-(1)/(a) at theta=(pi)/(2)

If x=a(1+cos theta),y=a(theta+sin theta), prove that (d^(2)y)/(dx^(2))=(-1)/(a) at theta=(pi)/(2)

If x=a(1-cos^3theta) , y=a\ sin^3theta , prove that (d^2y)/(dx^2)=(32)/(27\ a) at theta=pi/6 .

If x=a(1-cos^(3)theta),y=as in^(3)theta, prove that (d^(2)y)/(dx^(2))=(32)/(27a) at theta=(pi)/(6)

If x=a(theta+sintheta) , y=a(1+costheta) , prove that (d^2y)/(dx^2)=-a/(y^2) .

If x=a(theta+sintheta),y=a(1+costheta), Prove that (d^2y)/(dx^2)=-a/(y^2)

If x= a(costheta + sintheta), y= a(sintheta + costheta) , then (d^2y)/(dx^2) at theta = pi/4 .............

If x=2costheta-cos2\ theta and y=2sintheta-sin2\ theta , prove that (dy)/(dx)=tan((3theta)/2)

If x=a(theta+sin theta),y=a(1+cos theta), prove that (d^(2)y)/(dx^(2))=-(a)/(y^(2))

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)