แนวคิด ข้อ 5
$\begin{array}{l}
A + B = \pi - C\\
\dfrac{A}{2} + \dfrac{B}{2} = \dfrac{\pi }{2} - \dfrac{C}{2}\\
\tan \left( {\dfrac{A}{2} + \dfrac{B}{2}} \right) = \tan \left( {\dfrac{\pi }{2} - \dfrac{C}{2}} \right)\\
\dfrac{{\tan \dfrac{A}{2} + \tan \dfrac{B}{2}}}{{1 - \tan \dfrac{A}{2}\tan \dfrac{B}{2}}} = - \tan \dfrac{C}{2}\\
\tan \dfrac{A}{2} + \tan \dfrac{B}{2} = - \tan \dfrac{C}{2} + \tan \dfrac{A}{2}\tan \dfrac{B}{2}\tan \dfrac{C}{2}\\
\tan \dfrac{A}{2} + \tan \dfrac{B}{2} + \tan \dfrac{C}{2} = \tan \dfrac{A}{2}\tan \dfrac{B}{2}\tan \dfrac{C}{2}
\end{array}$
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