4 The parametric equations of a curve are
$$x = \frac { 1 } { \cos ^ { 3 } t } , \quad y = \tan ^ { 3 } t$$
where \(0 \leqslant t < \frac { 1 } { 2 } \pi\).
- Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \sin t\).
- Hence show that the equation of the tangent to the curve at the point with parameter \(t\) is \(y = x \sin t - \tan t\).