[sahaete]

แนวคิด ข้อ 2
$\begin{array}{l}
{\sin ^2}\frac{A}{2} + {\sin ^2}\frac{B}{2} + {\sin ^2}\frac{C}{2}\\
= \frac{1}{2}\left( {1 - \cos A} \right) + \frac{1}{2}\left( {1 - \cos B} \right) + \sin \frac{C}{2}\sin \frac{C}{2}\\
= 1 - \frac{1}{2}\left( {\cos A + \cos B} \right) + \sin \frac{C}{2}\sin \left( {\frac{\pi }{2} - \frac{{A + B}}{2}} \right)\\
= 1 - \frac{1}{2}\left( {2\cos \frac{{A + B}}{2}\cos \frac{{A - B}}{2}} \right) + \sin \frac{C}{2}\cos \frac{{A + B}}{2}\\
= 1 - \cos \left( {\frac{\pi }{2} - \frac{C}{2}} \right)\cos \frac{{A - B}}{2} + \sin \frac{C}{2}\cos \frac{{A + B}}{2}\\
= 1 - \sin \frac{C}{2}\cos \frac{{A - B}}{2} + \sin \frac{C}{2}\cos \frac{{A + B}}{2}\\
= 1 - \sin \frac{C}{2}\left( {\cos \frac{{A - B}}{2} -\cos \frac{{A + B}}{2}} \right)\\
= 1 - \sin \frac{C}{2}\left( {2\sin \frac{A}{2}\sin \frac{B}{2}} \right)\\
= 1 - 2\sin \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}
\end{array}$