(i)[3]
Demonstrate that $f(\theta) = \tan \theta$.
(ii)[4]
Hence prove that $\displaystyle \int_{\frac{\pi}{6}}^{\frac{\pi}{4}} f(\theta)\, d\theta = \frac{1}{2} \ln \frac{3}{2}$.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
Set $f(\theta) = \dfrac{1 - \cos 2\theta + \sin 2\theta}{1 + \cos 2\theta + \sin 2\theta}$.
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This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply double angle formulae and write the whole fraction in terms of $\sin\theta$ and $\cos\theta$” …
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