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  • In triangle ABC if <img alt="\tan\frac{A}{2}=\frac{3}{8}\ and\ \tan \frac{C}{2}=\frac{8}{9}" src="/latex-image/?%5Ctan%5Cfrac%7BA%7D%7B2%7D%3D%5Cfrac%7B3%7D%7B8%7D%5C%20and%5C%20%5Ctan%20%5Cfr

In triangle ABC if \tan\frac{A}{2}=\frac{3}{8}\ and\ \tan \frac{C}{2}=\frac{8}{9} then sides a,b,c are in 

Option: 1

A.P.


Option: 2

G.P.


Option: 3

H.P.


Option: 4

None of these


Answers (1)

best_answer

\\\tan\frac{A}{2}\tan \frac{C}{2}\\\\=\sqrt{\frac{(s-b)(s-c)}{s(s-a)}}\sqrt{\frac{(s-a)(s-b)}{s(s-c)}}\\ =\frac{s-b}{b}\\\\ =\frac{a+c-b}{a+b+c}=\frac{3}{9} \ \\\\(since\,\, \tan\frac{A}{2}=\frac{3}{8}\ \,\,and\ \tan \frac{C}{2}=\frac{8}{9})\\\\ \Rightarrow 3(a+c-b)=a+b+c\\ a+c=2b\\ a,b,c \ are\ in\ A.P.

Posted by

Devendra Khairwa

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