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

x= a(cos t + t sin t)


dx/dt = a(-sint+sin t +t cost) = at.cost



y= a(sin t - t cost)


dx/dt = a( cos t - cos t + t sin t )

= at sin t


dy/dx = dy/dt/dx/dt = at sin t/ at sin t = tan t



d^2y/dx^2 = sec^2t*1/ at cost

= 1/at* sec^3 t Ans.