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

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Trigonometrical Equations

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

A

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

B

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

C

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

D

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

Solution

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

Now apply $C/D$ and then proceed

Standard 11

Mathematics

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