Teorema cosinusului:
[tex]\cos A = \dfrac{b^2+c^2-a^2}{2bc} \Rightarrow \cos 90^\circ = \dfrac{b^2+c^2-a^2}{2bc} \Rightarrow \\ \\ \Rightarrow b^2+c^2-a^2 = 0[/tex]
Astfel:
[tex]\Rightarrow a^2+c^2-b^2 = 2a^2-2b^2= 2(a^2-b^2) = 2c^2 \\ \\ \Rightarrow a^2+b^2-c^2 = 2a^2-2c^2 = 2(a^2-c^2) = 2b^2\\ \\ \cos B = \dfrac{a^2+c^2-b^2}{2ac};\quad \cos C = \dfrac{a^2+b^2-c^2}{2ab}\\ \\ \Rightarrow \cos B+\cos C = \dfrac{2c^2}{2ac}+\dfrac{2b^2}{2ab}= \dfrac{c}{a}+\dfrac{b}{a} = \boxed{\dfrac{b+c}{a}}[/tex]
