In a ∆ABC , bcos2⁡C2+ccos2⁡B2 is equal to

A
$s$
B
$2 s$
C
$s / 2$
D
none of these

Solution:

we have ,

$\begin{array}{l} b \cos^{2} \frac{C}{2} + c \cos^{2} \frac{B}{2} \\ = \frac{b}{2} (1 + \cos C) + \frac{c}{2} (1 + \cos B) \\ = \frac{1}{2} (b + c + b \cos C + c \cos B) = \frac{1}{2} (b + c + a) = s \end{array}$

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