A) \[{{a}^{2}}+{{b}^{2}}-{{c}^{2}}\]
B) \[{{c}^{2}}+{{a}^{2}}-{{b}^{2}}\]
C) \[{{b}^{2}}-{{a}^{2}}-{{c}^{2}}\]
D) \[{{c}^{2}}-{{a}^{2}}-{{b}^{2}}\]
Correct Answer: B
Solution :
\[2ac\,\sin \left( \frac{A-B+C}{2} \right)\] \[=2ac\,\sin \left( \frac{180-2B}{2} \right)\] \[=2ac\sin ({{90}^{o}}-B)=2ac\,\cos \,B\] \[={{a}^{2}}+{{c}^{2}}-{{b}^{2}}\]
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