| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2014 |
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| Session | November |
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| Topic | Complex numbers 2 |
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6 Use de Moivre's theorem to show that
$$\cos 5 \theta \equiv \cos \theta \left( 16 \sin ^ { 4 } \theta - 12 \sin ^ { 2 } \theta + 1 \right)$$
By considering the equation \(\cos 5 \theta = 0\), show that the exact value of \(\sin ^ { 2 } \left( \frac { 1 } { 10 } \pi \right)\) is \(\frac { 3 - \sqrt { 5 } } { 8 }\).