| Exam Board | CAIE |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2018 |
| Session | November |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex numbers 2 |
7 (i) Use de Moivre's theorem to show that
$$\sin 8 \theta = 8 \sin \theta \cos \theta \left( 1 - 10 \sin ^ { 2 } \theta + 24 \sin ^ { 4 } \theta - 16 \sin ^ { 6 } \theta \right) .$$
(ii) Use the equation $\frac { \sin 8 \theta } { \sin 2 \theta } = 0$ to find the roots of
$$16 x ^ { 6 } - 24 x ^ { 4 } + 10 x ^ { 2 } - 1 = 0$$
in the form $\sin k \pi$, where $k$ is rational.\\
\hfill \mbox{\textit{CAIE FP1 2018 Q7}}