In any △ABC,Σcos⁡Abcos⁡C+ccos⁡B is equal to

In any $△ A B C, Σ \frac{\cos A}{b \cos C + c \cos B}$ is equal to

A
$a^{2} + b^{2} + c^{2}$
B
$\frac{a^{2} + b^{2} + c^{2}}{a b c}$
C
$\frac{a^{2} + b^{2} + c^{2}}{2 a b c}$
D
none of these

Solution:

Using Cosine and projection formulae, we have

$\sum \frac{\cos A}{b \cos C + c \cos B} = \frac{\cos A}{a} + \frac{\cos B}{b} + \frac{\cos C}{c} = \frac{a^{2} + b^{2} + c^{2}}{2 a b c}$

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