# OCR A Level: Further Pure 3 - Complex Numbers [January 2010 Q7]

Algebra Level 4

$$(\text{i})$$ Solve the equation $$\cos 6 \theta = 0$$, for $$0<\theta<\pi$$.

$$(\text{ii})$$ By using de Moivre's theorem, show that $\cos 6 \theta \equiv (2 \cos^2 \theta -1)(16 \cos^4 \theta - 16\cos^2 \theta +1).$

$$(\text{iii})$$ Hence find the exact value of $\cos \left (\dfrac{\pi}{12} \right ) \cos \left (\dfrac{5 \pi}{12} \right ) \cos \left (\dfrac{7 \pi}{12} \right ) \cos \left (\dfrac{11 \pi}{12} \right )$ justifying your answer.

If your answer to part $$(\text{iii})$$ is $$\dfrac{a}{b}$$ for co-prime integers $$a$$ and $$b$$, input $$a+b$$ as your answer.

###### This is part of the set OCR A Level Problems.
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