In triangle $\triangle \; ABC$ , if $2\frac{\cos A}{a} + \frac{\cos B}{b} + 2\frac{\cos C}{c} = \frac{a}{bc} + \frac{b}{ca}$ find angle $A$.
This is a quiz bee problem sent to me by my friend in FB. He asked me if I can do a solution for it. Well I tried several ways but I am out of idea now. The answer is 90 degree but what he asked, and I am also asking it now, is the solution for it.
Thank you.