A) \[s\]
B) \[2s\]
C) \[4\,s\]
D) \[3\,s\]
Correct Answer: A
Solution :
\[b\,{{\cos }^{2}}\frac{C}{2}+c\,{{\cos }^{2}}\frac{B}{2}\] \[=b{{\left( \sqrt{\frac{s(s-c)}{ab}} \right)}^{2}}+c{{\left( \sqrt{\frac{s(s-b)}{ca}} \right)}^{2}}\] \[=b\left( \frac{s(s-c)}{ab} \right)+c\left( \frac{s(s-b)}{ca} \right)\] \[=\frac{{{s}^{2}}-sc+{{s}^{2}}-sb}{a}=\frac{2{{s}^{2}}-s(b+c)}{a}\] \[=\frac{2{{s}^{2}}-s(2s-a)}{a}\] \[=\frac{2{{s}^{2}}-2{{s}^{2}}+sa}{a}=s\]
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