CAIE P2 2005 June — Question 7

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2005
SessionJune
TopicAddition & Double Angle Formulae
7
  1. By expanding \(\sin ( 2 x + x )\) and using double-angle formulae, show that $$\sin 3 x = 3 \sin x - 4 \sin ^ { 3 } x$$
  2. Hence show that $$\int _ { 0 } ^ { \frac { 1 } { 3 } \pi } \sin ^ { 3 } x d x = \frac { 5 } { 24 }$$
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