- In this question you must show all stages of your working.
\section*{Solutions relying entirely on calculator technology are not acceptable.}
- Use de Moivre's theorem to show that
$$\cos 5 x \equiv \cos x \left( a \sin ^ { 4 } x + b \sin ^ { 2 } x + c \right)$$
where \(a\), \(b\) and \(c\) are integers to be determined.
- Hence solve, for \(0 < \theta < \frac { \pi } { 2 }\)
$$\cos 5 \theta = \sin 2 \theta \sin \theta - \cos \theta$$
giving your answers to 3 decimal places.