Let A, B and C be the angles of a plane trian | vedclass

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(A) In a triangle $ABC$,the sum of angles is $A + B + C = \pi$.Therefore,$\frac{A+B}{2} = \frac{\pi}{2} - \frac{C}{2}$.Taking tangent on both sides,$\

Vedclass · Accepted Answer

$7/9$

Vedclass · Answer

(A) In a triangle $ABC$,the sum of angles is $A + B + C = \pi$.Therefore,$\frac{A+B}{2} = \frac{\pi}{2} - \frac{C}{2}$.Taking tangent on both sides,$	an \left( \frac{A+B}{2} ight) = 	an \left( \frac{\pi}{2} - \frac{C}{2} ight) = \cot \frac{C}{2}$.Using the formula $	an \left( \frac{A}{2} + \frac{B}{2} ight) = \frac{	an \frac{A}{2} + 	an \frac{B}{2}}{1 - 	an \frac{A}{2} 	an \frac{B}{2}}$,we get:$\cot \frac{C}{2} = \frac{\frac{1}{3} + \frac{2}{3}}{1 - (\frac{1}{3})(\frac{2}{3})} = \frac{1}{1 - \frac{2}{9}} = \frac{1}{\frac{7}{9}} = \frac{9}{7}$.Since $\cot \frac{C}{2} = \frac{9}{7}$,then $	an \frac{C}{2} = \frac{7}{9}$.

Let $A, B$ and $C$ be the angles of a plane triangle and $\tan \frac{A}{2} = \frac{1}{3}, \tan \frac{B}{2} = \frac{2}{3}$. Then $\tan \frac{C}{2}$ is equal to

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