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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Trignometry
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If in $\Delta ABC\; \tan\large\frac{A}{2}=\frac{5}{6}$ and $\tan\large\frac{C}{2}=\frac{2}{5}$ then $a,b,c$ are such that

$(a)\;b^2=ac\qquad(b)\;2b=a+c\qquad(c)\;2ac=b(a+c)\qquad(d)\;a+b=c$

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1 Answer

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Since $\tan\large\frac{A}{2}=\frac{5}{6}$
$\tan\large\frac{C}{2}=\frac{2}{5}$
$\tan\large\frac{A}{2}$$\tan\large\frac{C}{2}=\frac{5}{6}\times \frac{2}{5}$
$\large\frac{\Delta}{s(s-a)}.\frac{\Delta}{s(s-c)}=\frac{1}{3}$
$\large\frac{s-b}{s}=\frac{1}{3}$
$3s-3b=s$
$2s=3b$
$a+c=2b$
Hence (b) is the correct answer.
answered Oct 11, 2013 by sreemathi.v
 

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