Question

Let A, B and C are 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

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$A+B+C=\pi \therefore tan\left(\frac{A+B}{2}\right)=tan(\frac{\pi }{2}-\frac{C}{2})\Rightarrow \frac{tan\frac{A}{2}+tan\frac{B}{2}}{1-tan\frac{A}{2}.tan\frac{B}{2}}=cot\frac{C}{2}\Rightarrow \frac{\frac{1}{3}+\frac{2}{3}}{1-\frac{1}{3}.\frac{2}{3}}=\frac{9}{7}=cot\frac{C}{2}\therefore tan\frac{C}{2}=\frac{7}{9}$