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  • In a triangle ABC , if tan A/2 =5/6 , tan C/2=2/5 , then the sides a, b and c are in

In a triangle ABC , if tan A/2 =5/6 , tan C/2=2/5 , then the sides a, b and c are in

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Solution:   

                 an (fracA2) an (fracC2)=sqrtfrac(s-b)(s-c)s(s-a) imes sqrtfrac(s-a)(s-b)s(s-c)

        or                 frac56 imesfrac25=fracs-bs=frac2s-2b2s

      or                      frac13=fraca-b+ca+b+cRightarrow a+c=2b

      Rightarrow               a,b,c   are in A.P.

Posted by

Deependra Verma

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