[tex] \it Th. cos \Rightarrow \begin{cases} \it cosC=\dfrac{a^2+b^2-c^2}{2ab}
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\it cosB=\dfrac{a^2+c^2-b^2}{2ac} \end{cases} [/tex]
Membrul drept al egalității din enunț devine:
[tex] \it b\cdot \dfrac{a^2+b^2-c^2}{2ab} -c\cdot \dfrac{a^2+c^2-b^2}{2ac} =\dfrac{a^2+b^2-c^2-a^2-c^2+b^2}{2a} =
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= \dfrac{2b^2-2c^2}{2a}=\dfrac{2(b^2-c^2)}{2a} = \dfrac{b^2-c^2}{a} [/tex]