5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d5eb0ca8-92ba-466f-84f5-8fc36c168695-16_669_817_296_625}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of the curve with polar equation
$$r = 10 \cos \theta + \tan \theta \quad 0 \leqslant \theta < \frac { \pi } { 2 }$$
The point \(P\) lies on the curve where \(\theta = \frac { \pi } { 3 }\)
The region \(R\), shown shaded in Figure 1, is bounded by the initial line, the curve and the line \(O P\), where \(O\) is the pole.
Use algebraic integration to show that the exact area of \(R\) is
$$\frac { 1 } { 12 } ( a \pi + b \sqrt { 3 } + c )$$
where \(a\), \(b\) and \(c\) are integers to be determined.