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      Maths-
      General
      Easy

      Question

      In triangle A B C comma s squared t a n invisible function application A divided by 2 t a n invisible function application B divided by 2 t a n invisible function application C divided by 2 equals

      1. capital delta
      2. 2capital delta
      3. R
      4. 4R

      The correct answer is: capital delta


        In this question we have to find the value of s squared tan open parentheses A over 2 close parentheses tan open parentheses B over 2 close parentheses tan open parentheses C over 2 close parentheses
        We know that tan open parentheses A over 2 close parentheses space equals space fraction numerator S over denominator s minus a end fraction
tan open parentheses B over 2 close parentheses equals fraction numerator S over denominator s minus b end fraction
tan open parentheses C over 2 close parentheses equals fraction numerator S over denominator s minus c end fraction
        where S space equals space 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 space space comma space s space equals fraction numerator a plus b plus c over denominator 2 end fraction
        By putting these values in the given expression we get,
        s squared tan open parentheses A over 2 close parentheses tan open parentheses B over 2 close parentheses tan open parentheses C over 2 close parentheses
        =>s squared cross times fraction numerator S over denominator s minus a end fraction cross times fraction numerator S over denominator s minus b end fraction cross times fraction numerator S over denominator s minus c end fraction
        =>s squared cross times fraction numerator S cubed over denominator open parentheses s minus a close parentheses open parentheses s minus b close parentheses open parentheses s minus c close parentheses end fraction
        =>s squared cross times fraction numerator S cubed over denominator begin display style S squared over s end style end fraction

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