(i)[4]
Show that, $\frac{dy}{dx} = \sin t$.
(ii)[3]
Hence show that the equation of the tangent to the curve at the point with parameter $t$ is $y = x\sin t - \tan t$.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
For the curve, the parametric equations are $x = \frac{1}{\cos^3 t}$ and $y = \tan^3 t$, where $0 \le t < \frac{pi}{2}$.