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J & K CET Engineering J and K - CET Engineering Solved Paper-2008

  • question_answer
    In  any \[\Delta \,ABC\] under usual  notation, \[a(b\,\cos \,C-c\,\cos B)\] is equal to

    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 :

    \[a(b\,\cos \,C-c\,\cos \,B)=ab\,\left( \frac{{{a}^{2}}+{{b}^{2}}-{{c}^{2}}}{2ab} \right)\] \[-ac\left( \frac{{{a}^{2}}+{{c}^{2}}-{{b}^{2}}}{2ac} \right)\] \[=\frac{{{a}^{2}}+{{b}^{2}}-{{c}^{2}}}{2}-\frac{({{a}^{2}}+{{c}^{2}}-{{b}^{2}})}{2}\] \[={{b}^{2}}-{{c}^{2}}\]


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