CAIE P2 2024 March — Question 7

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2024
SessionMarch
TopicAddition & Double Angle Formulae
7
  1. Prove that $$\sin 2 \theta ( a \cot \theta + b \tan \theta ) \equiv a + b + ( a - b ) \cos 2 \theta$$ where \(a\) and \(b\) are constants.
  2. Find the exact value of \(\int _ { \frac { 1 } { 12 } \pi } ^ { \frac { 1 } { 6 } \pi } \sin 2 \theta ( 5 \cot \theta + 3 \tan \theta ) d \theta\).
  3. Solve the equation \(\sin \frac { 2 } { 3 } \alpha \left( 2 \cot \frac { 1 } { 3 } \alpha + 7 \tan \frac { 1 } { 3 } \alpha \right) = 11\) for \(- \pi < \alpha < \pi\).
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Q1 4 Q2 Q3 Q5 Q6 Q7