A) \[3\]
B) \[2\]
C) \[1\]
D) \[0\]
Correct Answer: C
Solution :
\[\tan \frac{A}{2}.\tan \frac{B}{2}+\tan \frac{B}{2}.\tan \frac{C}{2}+\tan \frac{C}{2}.\tan \frac{A}{2}\] \[\sqrt{\frac{(s-b)\,(s-c)}{s(s-a)}}\,\,\sqrt{\frac{(s-a)\,(s-c)}{s\,(s-b)}}\] \[+\sqrt{\frac{(s-a)\,(s-c)}{s(s-b)}}\,\,\sqrt{\frac{(s-a)\,(s-b)}{s\,(s-a)}}\] \[=\frac{s-c}{s}+\frac{s-a}{s}+\frac{s-b}{s}\] \[=\frac{3s-(a+b+c)}{s}=\frac{3s-2s}{s}\] \[(\because \,\,2s=a+b+c)\] \[=\frac{s}{s}=1\]
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