If A + B + C = & sin , ( A , , + , ,C 2 ) = k ,sin,C 2 then tan ,… - Vidyadip

MCQ

If $A + B + C = \pi$ & $sin\, \left( {A\,\, + \,\,\frac{C}{2}} \right) = k \,sin,\frac{C}{2}$ then $tan\, \frac{A}{2} \,tan \, \frac{B}{2}=$

✓
$\frac{{k\,\, - \,\,1}}{{k\,\, + \,\,1}}$
B
$\frac{{k\,\, + \,\,1}}{{k\,\, - \,\,1}}$
C
$\frac{k}{{k\,\, + \,\,1}}$
D
$\frac{{k\,\, + \,\,1}}{k}$

✓

Answer

Correct option: A.

$\frac{{k\,\, - \,\,1}}{{k\,\, + \,\,1}}$

a
$\frac{{\sin \left( {A + \frac{C}{2}} \right)}}{{\sin \frac{C}{2}}} = K$

Now apply $C/D$ and then proceed

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