CAIE P3 2004 June — Question 5

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2004
SessionJune
TopicAddition & Double Angle Formulae
5
  1. Prove the identity $$\sin ^ { 2 } \theta \cos ^ { 2 } \theta \equiv \frac { 1 } { 8 } ( 1 - \cos 4 \theta )$$
  2. Hence find the exact value of $$\int _ { 0 } ^ { \frac { 1 } { 3 } \pi } \sin ^ { 2 } \theta \cos ^ { 2 } \theta \mathrm {~d} \theta$$
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