CAIE P3 2019 June — Question 6

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2019
SessionJune
TopicAddition & Double Angle Formulae
6
  1. By first expanding \(\sin ( 2 x + x )\), show that \(\sin 3 x \equiv 3 \sin x - 4 \sin ^ { 3 } x\).
  2. Hence, showing all necessary working, find the exact value of \(\int _ { 0 } ^ { \frac { 1 } { 3 } \pi } \sin ^ { 3 } x \mathrm {~d} x\).
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