Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
26,\\
b.\cos C + c.\cos B\\
= b.\dfrac{{{a^2} + {b^2} - {c^2}}}{{2ab}} + c.\dfrac{{{a^2} + {c^2} - {b^2}}}{{2ac}}\\
= \dfrac{{{a^2} + {b^2} - {c^2}}}{{2a}} + \dfrac{{{a^2} + {c^2} - {b^2}}}{{2a}}\\
= \dfrac{{\left( {{a^2} + {b^2} - {c^2}} \right) + \left( {{a^2} + {c^2} - {b^2}} \right)}}{{2a}}\\
= \dfrac{{2{a^2}}}{{2a}} = a\\
27,\\
\sin B = 2\sin A.\cos C\\
\Leftrightarrow \sin B = \sin \left( {A + C} \right) + \sin \left( {A - C} \right)\\
\Leftrightarrow \sin B = \sin \left( {180^\circ - A - B} \right) + \sin \left( {A - C} \right)\\
\Leftrightarrow \sin B = \sin B + \sin \left( {A - C} \right)\\
\Leftrightarrow \sin \left( {A - C} \right) = 0\\
\Rightarrow \widehat A = \widehat C
\end{array}\)
