9709 P31 - Nov 2009 - Q5
1720
(i) Prove the identity \(\cos 4\theta - 4 \cos 2\theta + 3 \equiv 8 \sin^4 \theta\).
(ii) Using this result find, in simplified form, the exact value of \(\int_{\frac{1}{6}\pi}^{\frac{1}{3}\pi} \sin^4 \theta \, d\theta\).
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