A) \[{{b}^{2}}-{{c}^{2}}\]
B) \[{{c}^{2}}-{{b}^{2}}\]
C) \[\frac{{{b}^{2}}-{{c}^{2}}}{2}\]
D) \[\frac{{{c}^{2}}-{{b}^{2}}}{2}\]
Correct Answer: A
Solution :
\[a(b\,\cos \,C-c\,\cos \,B)=ab\,\left( \frac{{{a}^{2}}+{{b}^{2}}-{{c}^{2}}}{2ab} \right)\] \[-ac\left( \frac{{{a}^{2}}+{{c}^{2}}-{{b}^{2}}}{2ac} \right)\] \[=\frac{{{a}^{2}}+{{b}^{2}}-{{c}^{2}}}{2}-\frac{({{a}^{2}}+{{c}^{2}}-{{b}^{2}})}{2}\] \[={{b}^{2}}-{{c}^{2}}\]You need to login to perform this action.
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