<ol class="i-list"><li data-list-item-id="item-1760428154951-wp6mixcgj" data-list-item-path="item-1760428154951-wp6mixcgj"><div class="list-item-paragraph">Given that&nbsp;$t=\tan \frac{1}{2}x$ where&nbsp;$0 &lt; x &lt; \pi $, show that&nbsp;$\sin x=\frac{2t}{1+{{t}^{2}}}$.<span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-1760428155687-sg2yak12n" data-list-item-path="item-1760428155687-sg2yak12n"><div class="list-item-paragraph">By using the substitution $t=\tan \frac{1}{2}x$, show that&nbsp;$\displaystyle\displaystyle \displaystyle\int_{0}^{\frac{\pi }{2}}{\frac{1}{2+\sin x}}\,\mathrm{d}x=\frac{\sqrt{3}}{9}\pi $.<span class="inline-marks">[5]</span></div></li></ol>

Given that $t=\tan \frac{1}{2}x$ where $0 < x < \pi $, show that $\sin x=\frac{2t}{1+{{t}^{2}}}$.

By using the substitution $t=\tan \frac{1}{2}x$, show that $\displaystyle\displaystyle \displaystyle\int_{0}^{\frac{\pi }{2}}{\frac{1}{2+\sin x}}\,\mathrm{d}x=\frac{\sqrt{3}}{9}\pi $.

2022 TJC Promo Q4

2022 TJC Promo Q4

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