Discussion Forum

1)

In $\triangle ABC$  , with the usual notations , if 

$(\tan \frac{A}{2})(\tan \frac{B}{2})=\frac{3}{4}$   then a+b=.....

Answer:

Option C

Explanation:

 We have , in $\triangle ABC$

   $(\tan \frac{A}{2})(\tan \frac{B}{2})=\frac{3}{4}$ 

  $\Rightarrow \sqrt{\frac{(s-b)(s-c)}{s(s-a)}}\sqrt{\frac{(s-a)(s-c)}{s(s-b)}}=\frac{3}{4}$

$\Rightarrow \sqrt{\frac{(s-b)(s-c)(s-a)(s-c)}{s(s-a).s(s-b)}}=\frac{3}{4}$

$\Rightarrow\frac{(s-c)}{s}=\frac{3}{4}\Rightarrow\frac{\frac{a+b+c}{2}-c}{\frac{a+b+c}{2}}=\frac{3}{4}$

  $\Rightarrow$   $ \frac{a+b-c}{a+b+c}=\frac{3}{4}$

$\Rightarrow $    $4a+4b-4c=3a+3b+3c$

$\Rightarrow $        a+b= 7c