4 The parametric equations of a curve are

$$x = \frac { 1 } { \cos ^ { 3 } t } , \quad y = \tan ^ { 3 } t$$

where $0 \leqslant t < \frac { 1 } { 2 } \pi$.\\
(i) Show that $\frac { \mathrm { d } y } { \mathrm {~d} x } = \sin t$.\\
(ii) Hence show that the equation of the tangent to the curve at the point with parameter $t$ is $y = x \sin t - \tan t$.

\hfill \mbox{\textit{CAIE P3 2014 Q4}}