AQA C4 2005 June — Question 6

Exam BoardAQA
ModuleC4 (Core Mathematics 4)
Year2005
SessionJune
TopicAddition & Double Angle Formulae
6
  1. Express \(\sin 2 x\) in terms of \(\sin x\) and \(\cos x\).
  2. Using the identity \(\cos ( A + B ) = \cos A \cos B - \sin A \sin B\) :
    1. express \(\cos 2 x\) in terms of \(\sin x\) and \(\cos x\);
    2. show, by writing \(3 x\) as \(( 2 x + x )\), that $$\cos 3 x = 4 \cos ^ { 3 } x - 3 \cos x$$
  3. Show that \(\int _ { 0 } ^ { \frac { \pi } { 2 } } \cos ^ { 3 } x \mathrm {~d} x = \frac { 2 } { 3 }\).
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