Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\frac{a}{{\sin A}} = \frac{b}{{\sin B}} = \frac{c}{{\sin C}} = 2R \Rightarrow \frac{a}{b} = \frac{{\sin A}}{{\sin B}}\\
\frac{{\tan A}}{{\tan B}} = \frac{{\sin A}}{{\cos A}}:\frac{{\sin B}}{{\cos B}} = \frac{{\sin A}}{{\sin B}}.\frac{{\cos B}}{{\cos A}}\\
= \frac{a}{b}.\frac{{\frac{{{a^2} + {c^2} - {b^2}}}{{2ac}}}}{{\frac{{{b^2} + {c^2} - {a^2}}}{{2bc}}}} = \frac{a}{b}.\frac{{b\left( {{a^2} + {c^2} - {b^2}} \right)}}{{a.\left( {{b^2} + {c^2} - {a^2}} \right)}} = \frac{{{a^2} + {c^2} - {b^2}}}{{{b^2} + {c^2} - {a^2}}}
\end{array}\)
