If `x=a(cost+tsint)` and `y=a(sint-tcost)`, find `(d^2y)/(dx^2)`

Explanation

`x=a(cost+tsint)`
`implies(dx)/(dt)=a(-sint+sint+tcost)=atcost`
and `y=a(sint-tcost)`
`implies(dy)/(dx)=a[cost-(-tsint+cost)]=atsint`
` :. (dy)/(dx)=(dy//dt)/(dx//dt)=(atsint)/(atcost)=tant`
`(d^(2)y)/(dx^(2))=(d)/(dx)((dy)/(dx))=(d)/(dx)(tant)`
`implies=(d)/(dx)(tant)*(dt)/(dx)`
`=sec^(2)t*(1)/(atcost)=(1)/(at)sec^(3)t`