CAIE P2 2021 November — Question 7

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2021
SessionNovember
TopicAddition & Double Angle Formulae
7
  1. By first expanding \(\cos ( 2 \theta + \theta )\), show that \(\cos 3 \theta \equiv 4 \cos ^ { 3 } \theta - 3 \cos \theta\).
  2. Find the exact value of \(2 \cos ^ { 3 } \left( \frac { 5 } { 18 } \pi \right) - \frac { 3 } { 2 } \cos \left( \frac { 5 } { 18 } \pi \right)\).
  3. Find \(\int \left( 12 \cos ^ { 3 } x - 4 \cos ^ { 3 } 3 x \right) \mathrm { d } x\).
    If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.
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