In triangle ABC, prove that `(b/c+c/b) cosA +(a/b+b/a) cos C+(a/c+c/a)cosB=3`

Explanation

To prove the identity

\[ \left(\frac{b}{c} + \frac{c}{b}\right) \cos A + \left(\frac{a}{b} + \frac{b}{a}\right) \cos C + \left(\frac{a}{c} + \frac{c}{a}\right) \cos B = 3 \]

in triangle ABC, we will use the projection formulas related to the sides and angles of the triangle.

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