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Question Number 21116 by mondodotto@gmail.com last updated on 13/Sep/17

Answered by Tinkutara last updated on 13/Sep/17

$$\tan \mathrm{A}=\frac{3}{4}\Rightarrow \sin \mathrm{A}=\frac{3}{5},\cos \mathrm{A}=\frac{4}{5}$$$$\cos \mathrm{A}={2\cos }^2\frac{\mathrm{A}}{2}-1$$$${\cos }^2\frac{\mathrm{A}}{2}=\frac{1+\cos \mathrm{A}}{2}=\frac{9}{10}\Rightarrow \cos \frac{\mathrm{A}}{2}=\frac{3}{\sqrt{10}}$$$$\therefore \sin \frac{\mathrm{A}}{2}=\frac{1}{\sqrt{10}}$$

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