cmr (tanA + tanB + tanC).R= abc/a²+b²+c² Giúp mình vs ạ mình cảm ơn

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1. Giải thích các bước giải:

    Ta có:

   \(\begin{array}{l}
   \dfrac{a}{{\sin A}} = \dfrac{b}{{\sin B}} = \dfrac{c}{{\sin C}} = 2R\\
    \Rightarrow \left\{ \begin{array}{l}
   a = 2R.\sin A\\
   b = 2R.\sin B\\
   c = 2R.\sin C
   \end{array} \right.\\
   \left( {\tan A + \tan B + \tan C} \right).R\\
    = \left( {\dfrac{{\sin A}}{{\cos A}} + \dfrac{{\sin B}}{{\cos B}} + \dfrac{{\sin C}}{{\cos C}}} \right).R\\
    = \dfrac{{\sin A.R}}{{\cos A}} + \dfrac{{\sin B.R}}{{\cos B}} + \dfrac{{\sin C.R}}{{\cos C}}\\
    = \dfrac{a}{{2\cos A}} + \dfrac{b}{{2\cos B}} + \dfrac{c}{{2\cos C}}\\
    = \dfrac{a}{{2.\dfrac{{{b^2} + {c^2} – {a^2}}}{{2bc}}}} + \dfrac{b}{{2.\dfrac{{{c^2} + {a^2} – {b^2}}}{{2ca}}}} + \dfrac{c}{{2.\dfrac{{{a^2} + {b^2} – {c^2}}}{{2ab}}}}\\
    = \dfrac{{abc}}{{{b^2} + {c^2} – {a^2}}} + \dfrac{{abc}}{{{c^2} + {a^2} – {b^2}}} + \dfrac{{abc}}{{{a^2} + {b^2} – {c^2}}}
   \end{array}\)

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