In a triangle ABC , with usual notations, $\frac{\cos B+\cos C}{b+c}+\frac{\cos A}{a}$ has the value

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Aicharya · Accepted Answer

$\begin{aligned} & \frac{\cos B+\cos C}{b+c}+\frac{\cos A}{a} \ & =\frac{a \cos B+a \cos C+b \cos A+c \cos A}{a(b+c)} \ & =\frac{(a \cos B+b \cos A)+(a \cos C+c \cos A)}{a(b+c)}\end{aligned}$ $\begin{aligned} & =\frac{c+b}{a(b+c)} \ & =\frac{1}{a} \end{aligned}$ ...[By projection rule]

In a triangle ABC , with usual notations, $\frac{\cos B+\cos C}{b+c}+\frac{\cos A}{a}$ has the value

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