(i)[4]
Prove that $\tan 2\theta - \tan \theta \equiv \tan \theta \sec 2\theta$.
(ii)[4]
Hence show that evaluating $\int_{0}^{\frac{\pi}{6}} \tan \theta \sec 2\theta \, d\theta$ gives $\frac{1}{2} \ln \frac{3}{2}$.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use a $\tan 2A$ formula so that the LHS is written in terms of $\tan\theta$” …
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