<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text"></span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Show that $\tan 2\theta =\frac{2\tan \theta }{1-{{\tan }^{2}}\theta }$ using the addition formula from the List of Formulae (MF26).</span></div><p style="text-align: right;">[1]</p></li><li><div class="list-item-content"><span class="list-item-text">By using the substitution $x=\tan \theta $, or otherwise, find the exact value of  $\int_{0}^{1}{{{\tan }^{-1}}\left( \frac{2x}{1-{{x}^{2}}} \right)}\,\mathrm{d}x$.</span></div><p style="text-align: right;">[5]</p></li></ol></li><li><div class="list-item-content"><span class="list-item-text">Find the exact value of $\int_{-1}^{1}{\frac{2+\left| x \right|}{2+x}\mathrm{d}x}$.</span></div><p style="text-align: right;">[4]</p></li></ol>

Show that $\tan 2\theta =\frac{2\tan \theta }{1-{{\tan }^{2}}\theta }$ using the addition formula from the List of Formulae (MF26).

By using the substitution $x=\tan \theta $, or otherwise, find the exact value of  $\displaystyle\displaystyle \int_{0}^{1}{{{\tan }^{-1}}\left( \frac{2x}{1-{{x}^{2}}} \right)}\,\mathrm{d}x$.

Find the exact value of $\displaystyle\displaystyle \int_{-1}^{1}{\frac{2+\left| x \right|}{2+x}\mathrm{d}x}$.

2020 NYJC J2 CT P1 Q6

2020 NYJC J2 CT P1 Q6

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