JEE Main & Advanced Mathematics Trigonometric Equations Question Bank Relation between sides and angles, Solutions of triangles

  • question_answer
    In a \[\Delta ABC\], if \[2s=a+b+c\]and \[(s-b)(s-c)=\] \[x{{\sin }^{2}}\frac{A}{2},\] then x = [MP PET 1992]

    A) bc

    B) ca

    C) ab

    D) abc

    Correct Answer: A

    Solution :

     \[\sin \frac{A}{2}=\sqrt{\frac{(s-b)(s-c)}{bc}}\] \[\Rightarrow bc{{\sin }^{2}}\frac{A}{2}=(s-b)(s-c)\] Hence\[x=bc\].


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