2. Solved Papers
  3. Manipal Engineering

Manipal Engineering Manipal Engineering Solved Paper-2012

  • question_answer
    If\[k\]be the perimeter of the\[\Delta \,\,ABC\], then\[b{{\cos }^{2}}\frac{C}{2}+c{{\cos }^{2}}\frac{B}{2}\]is equal to

    A) \[k\]                                     

    B) \[2k\]

    C) \[\frac{k}{2}\]                   

    D)         None of these

    Correct Answer: C

    Solution :

    \[b{{\cos }^{2}}\frac{C}{2}+c{{\cos }^{2}}\frac{B}{2}\]                 \[=\frac{b}{2}(1+\cos C)+\frac{c}{2}(1+\cos B)\]                 \[=\frac{b}{2}+\frac{c}{2}+\frac{1}{2}(b\cos C+c\cos B)\]                 \[=\frac{b}{2}+\frac{c}{2}+\frac{a}{2}\]  \[(\because \,\,a=b\cos C+c\cos B)\]                 \[=\frac{a+b+c}{2}=\frac{k}{2}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner