2025 MI P1 Q1

In this question you may use expansions from the List of Formulae (MF27).

It is given that \(\mathrm{f}(\theta) = \frac{1}{3 - \sin \theta}\), for \(\theta > 0\). Show that when \(\theta\) is sufficiently small,

\(\mathrm{f}(\theta) \approx p + q\theta + r\theta^2\), where \(p\), \(q\) and \(r\) are exact constants to be determined.[4]