9709 P31 - Jun 2019 - Q6
1728
(i) By first expanding \(\sin(2x + x)\), show that \(\sin 3x \equiv 3 \sin x - 4 \sin^3 x\).
(ii) Hence, showing all necessary working, find the exact value of \(\int_0^{\frac{1}{3}\pi} \sin^3 x \, dx\).
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