A) \[7/9\]
B) \[2/9\]
C) \[1/3\]
D) \[2/3\]
Correct Answer: A
Solution :
\[A+B+C=\pi \] |
\[\therefore \,\,\,\,\tan \left( \frac{A+B}{2} \right)=\tan \left( \frac{\pi }{2}-\frac{C}{2} \right)\] |
\[\Rightarrow \,\,\,\,\frac{\tan \frac{A}{2}+\tan \frac{B}{2}}{1-\tan \frac{A}{2}.\tan \frac{B}{2}}=\cot \,\frac{C}{2}\] |
\[\Rightarrow \,\,\frac{\frac{1}{3}+\frac{2}{3}}{1-\frac{1}{3}.\frac{2}{3}}=\frac{9}{7}=\cot \,\frac{C}{2}\] |
\[\therefore \,\tan \,\frac{C}{2}=\frac{7}{9}\]. |
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