Show that any triangle with standard labeling...

Question

a^2+b^2+c^2/2abc = cos(alpha)/a + cos(beta)/b + cos(gamma)/c

I don't get it. Can someone please help me.



Start here with the law of cosines:
a^2 = b^2 + c^2 -2bc Cos A
b^2 = a^2 + c^2 -2ac Cos B
c^2 = a^2 + b^2 - 2ab Cos C

Add the three equations. divide both sides by 2abc