- A curve has parametric equations
$$x = \cos 2 t , \quad y = \operatorname { cosec } t , \quad 0 < t < \frac { \pi } { 2 }$$
The point \(P\) on the curve has \(x\)-coordinate \(\frac { 1 } { 2 }\).
- Find the value of the parameter \(t\) at \(P\).
- Show that the tangent to the curve at \(P\) has the equation
$$y = 2 x + 1$$