CAIE P3 2019 November — Question 9

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2019
SessionNovember
TopicAddition & Double Angle Formulae
9
  1. By first expanding \(\cos ( 2 x + x )\), show that \(\cos 3 x \equiv 4 \cos ^ { 3 } x - 3 \cos x\).
  2. Hence solve the equation \(\cos 3 x + 3 \cos x + 1 = 0\), for \(0 \leqslant x \leqslant \pi\).
  3. Find the exact value of \(\int _ { \frac { 1 } { 6 } \pi } ^ { \frac { 1 } { 3 } \pi } \cos ^ { 3 } x \mathrm {~d} x\).
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