We have
`x=3sin t-sin 3t`
`rArr (dx)/(dt)=3 cos t - 3 cos 3t." …(i)"`
And, `y=3cos t-cos 3t`
`rArr (dy)/(dx)=-3sin t + 3 sin 3t." …(ii)"`
`therefore(dy)/(dx)=((dy//dt))/((dx//dt))=(-3 sin t+3sin 3t)/(3cos t-3 cos 3t)=(sin 3t-sint)/(cos t -cos 3t)`
`=(2cos 2tsint)/(2sin 2t sin t)=cot 2t.`
`therefore(d^(2)y)/(dx^(2))=-2"cosec"^(2)2t.(dt)/(dx)=(-2"cosec"^(2)2t)/((dx//dt))=(-2"cosec"^(2)2t)/(3(cost-cos3t)).`
`therefore((d^(2)y)/(dx^(2)))_((t=(pi)/(3)))=(-2"cosec"^(2)(2pi//3))/(3cos.(pi)/(3)-cos pi)=-2xx((2)/(sqrt3))^(2).(1)/(3((1)/(2)+1))`
`(-2xx(4)/(3)xx(2)/(9))=(-16)/(27).`
