AQA C4 2007 January — Question 3

Exam BoardAQA
ModuleC4 (Core Mathematics 4)
Year2007
SessionJanuary
TopicAddition & Double Angle Formulae
3
  1. Express \(\cos 2 x\) in terms of \(\sin x\).
    1. Hence show that \(3 \sin x - \cos 2 x = 2 \sin ^ { 2 } x + 3 \sin x - 1\) for all values of \(x\).
    2. Solve the equation \(3 \sin x - \cos 2 x = 1\) for \(0 ^ { \circ } < x < 360 ^ { \circ }\).
  3. Use your answer from part (a) to find \(\int \sin ^ { 2 } x \mathrm {~d} x\).
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