Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\frac{a}{{\sin A}} = \frac{b}{{\sin B}} = \frac{c}{{\sin C}} = 2R \Rightarrow \frac{{\sin C}}{{\sin A}} = \frac{c}{a};\,\,\,\,\frac{{\sin B}}{{\sin A}} = \frac{b}{a}\\
\frac{{\sin C.\cos B - \sin B.\cos C}}{{\sin A}}\\
= \frac{{\sin C}}{{\sin A}}.\cos B - \frac{{{\mathop{\rm sinB}\nolimits} }}{{\sin A}}.\cos C\\
= \frac{c}{a}.\frac{{{a^2} + {c^2} - {b^2}}}{{2ac}} - \frac{b}{a}.\frac{{{a^2} + {b^2} - {c^2}}}{{2ab}}\\
= \frac{{{a^2} + {c^2} - {b^2}}}{{2{a^2}}} - \frac{{{a^2} + {b^2} - {c^2}}}{{2{a^2}}}\\
= \frac{{{c^2} - {b^2}}}{{{a^2}}}
\end{array}\)
