9709 P31 - Jun 2021 - Q4
1725
(a) Prove that \(\frac{1 - \cos 2\theta}{1 + \cos 2\theta} \equiv \tan^2 \theta\).
(b) Hence find the exact value of \(\int_{\frac{1}{6}\pi}^{\frac{1}{3}\pi} \frac{1 - \cos 2\theta}{1 + \cos 2\theta} \, d\theta\).
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