CAIE P3 2016 November — Question 5

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2016
SessionNovember
TopicIntegration by Substitution
5
  1. Prove the identity \(\tan 2 \theta - \tan \theta \equiv \tan \theta \sec 2 \theta\).
  2. Hence show that \(\int _ { 0 } ^ { \frac { 1 } { 6 } \pi } \tan \theta \sec 2 \theta \mathrm {~d} \theta = \frac { 1 } { 2 } \ln \frac { 3 } { 2 }\).
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