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  • In triangle ABC if <img alt="\sin^2 \frac{B}{2}=\sin\frac{A}{2}. \sin \frac{C}{2}" src="/latex-image/?%5Csin%5E2%20%5Cfrac%7BB%7D%7B2%7D%3D%5Csin%5Cfrac%7BA%7D%7B2%7D.%20%5Csin%20%5Cfrac%7BC%7

In triangle ABC if \sin^2 \frac{B}{2}=\sin\frac{A}{2}. \sin \frac{C}{2} then \frac{s-a}{a},\frac{s-b}{b},\frac{s-c}{c} are in

Option: 1

A.P.


Option: 2

G.P.


Option: 3

H.P.


Option: 4

None of these


Answers (1)

best_answer

 

\\Given,\,\, \sin^2 \frac{B}{2}=\sin \frac{A}{2}\sin \frac{C}{2}\\\\ \frac{(s-c)(s-a)}{ac}=\sqrt{\frac{(s-b)(s-c)}{bc}}\sqrt{\frac{(s-a)(s-b)}{ab}}\\\\ \sqrt{\frac{(s-c)(s-a)}{ac}}=\frac{(s-b)}{b}\\\\ \frac{(s-c)(s-a)}{ac}=\left(\frac{(s-b)}{b}\right)^2\\

\frac{s-a}{a},\frac{s-b}{b},\frac{s-c}{c} are in G.P.

Posted by

vishal kumar

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