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    Maths-
    General
    Easy

    Question

    In triangle A B C comma a b c sin invisible function application A divided by 2 space sin invisible function application B divided by 2 space sin invisible function application C divided by 2 equals

    1. capital delta squared
    2. capital delta squared divided by s
    3. capital delta to the power of 2 s end exponent
    4. s divided by capital delta squared

    hintHint:

    In this question we will first we will use
    sin open parentheses A over 2 close parentheses equals square root of fraction numerator left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis over denominator b c end fraction end root sin open parentheses B over 2 close parentheses equals square root of fraction numerator left parenthesis s minus a right parenthesis left parenthesis s minus c right parenthesis over denominator a c end fraction end root sin open parentheses C over 2 close parentheses equals square root of fraction numerator left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis over denominator a b end fraction end root
    then we will use
    increment equals square root of s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis end root

    The correct answer is: capital delta squared divided by s

      In this question we have to find the value of a b c sin open parentheses A over 2 close parentheses sin open parentheses B over 2 close parentheses sin open parentheses C over 2 close parentheses
      We know that
      sin open parentheses A over 2 close parentheses equals square root of fraction numerator left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis over denominator b c end fraction end root sin open parentheses B over 2 close parentheses equals square root of fraction numerator left parenthesis s minus a right parenthesis left parenthesis s minus c right parenthesis over denominator a c end fraction end root sin open parentheses C over 2 close parentheses equals square root of fraction numerator left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis over denominator a b end fraction end root
      and increment equals square root of s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis end root
      By substituting these value in the given expression
      a b c cross times square root of fraction numerator left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis over denominator b c end fraction end root cross times square root of fraction numerator left parenthesis s minus a right parenthesis left parenthesis s minus c right parenthesis over denominator a c end fraction end root cross times square root of fraction numerator left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis over denominator a b end fraction end root
      =>a b c cross times square root of fraction numerator left parenthesis s minus a right parenthesis squared left parenthesis s minus b right parenthesis squared left parenthesis s minus c right parenthesis squared over denominator a squared b squared c squared end fraction end root
      => left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis
      =>increment squared over s

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