Cubed sine from a triple angle identity

Cubed sine from a triple angle identity

IB Year 6 | Grade 12
  1. Use complex number methods to show that \(\sin 3\theta = 3\sin\theta - 4\sin^3\theta\).
  2. Hence find the exact value of \(\sin^3\dfrac{5\pi}{12}\).

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Answer:(a) Shown; \(\sin3\theta=3\sin\theta-4\sin^3\theta\) (b) \(\dfrac{3\sqrt6+5\sqrt2}{16}\)

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