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

  • question_answer
    In triangle \[ABC\]if \[a,b,c\]are in A. P., then the value of \[\frac{\sin \frac{A}{2}\sin \frac{C}{2}}{\sin \frac{B}{2}}=\] [AMU 1995]

    A) 1

    B) 1/2

    C) 2

    D) -1

    Correct Answer: B

    Solution :

    \[\frac{\sin \frac{A}{2}\sin \frac{C}{2}}{\sin \frac{B}{2}}=\sqrt{\frac{ac(s-b)(s-c)(s-b)(s-a)}{(s-a)(s-c)bc\times ab}}=\frac{s-b}{b}\] But a, b and c are in A. P. Þ \[2b=a+c\] Hence\[\frac{s-b}{b}=\frac{\frac{3b}{2}-b}{b}=\frac{1}{2}\].


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