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  4. In Δ A B C,(r2+r3) cot ((B+C/2))=

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Q. In$ \Delta A B C,\left(r_{2}+r_{3}\right) \cot \left(\frac{B+C}{2}\right)=$

AP EAMCETAP EAMCET 2019

Solution:

Given, in $\Delta A B C$
$\left(r_{2}+r_{3}\right) \cot \left(\frac{B+c}{2}\right)=\left(\frac{\Delta}{s-b}+\frac{\Delta}{s-c}\right) \tan \frac{A}{2}$
$=\frac{\Delta(s-c+s-b)}{(s-b)(s-c)} \frac{\Delta}{s(s-a)}$
$ =2 s-b-c=a$