Phương pháp giải:

\(\begin{array}{l}\widehat A + \widehat B + \widehat C = 180^\circ \\\sin \left( {180^\circ  - \widehat A} \right) = \sin \widehat A\\\cos \left( {90^\circ  - \widehat A} \right) = \sin \widehat A\end{array}\)

Lời giải chi tiết:

\(\begin{array}{l}\widehat A + \widehat B + \widehat C = 180^\circ \\ \Rightarrow \sin \left( {\widehat B + \widehat C} \right) = \sin \left( {180^\circ  - \widehat A} \right) = \sin \widehat A\\\cos \left( {\dfrac{{\widehat A + \widehat C}}{2}} \right) = \cos \left( {90^\circ  - \dfrac{{\widehat B}}{2}} \right) = \sin \dfrac{{\widehat B}}{2}\\\cos \left( {\widehat A + \widehat B} \right) =  - \cos \widehat C\end{array}\)