Question

Buna,am nevoie de rezolvare,URGENT
Sa se demonstreze ca intr-un triunghi oarecare ABC au loc relatiile:
a*b* cos(C) + a*c cos(B) + b*c cos(A) =(a^2 + b^2 +c^2)/2

Answer 1

trebuie doar aplicata teorema cosinusului:
[tex]\cos C=\frac{b^2+a^2-c^2}{2ab};\ \cos B=\frac{a^2+c^2-b^2}{2ac};\ \cos A=\frac{b^2+c^2-a^2}{2bc}\\ \text{Inlocuim in relatia data}\\ ab\frac{b^2+a^2-c^2}{2ab}+ac\frac{a^2+c^2-b^2}{2ac}+bc\frac{b^2+c^2-a^2}{2bc}=\\ =\frac{a^2+b^2-c^2}{2}+\frac{a^2+c^2-b^2}{2}+\frac{c^2+b^2-a^2}{2}=\frac{a^2+b^2+c^2}{2}[/tex]