Answer
The required value of the tan 2B is $\frac{2\tan \,B}{1-{{\tan }^{2}}B}$.
Work Step by Step
In order to find the value of tan 2B, the double angle formula is used:
$\tan \left( \alpha +\beta \right)=\frac{\tan \alpha +\tan \beta }{1-\tan \alpha \tan \beta }$
Now, consider $\alpha $ and $\beta $ as B; then the formula becomes:
$\begin{align}
& \tan \left( B+B \right)=\frac{\tan B+\tan \,B}{1-\tan B\tan B} \\
& =\frac{2\tan \,B}{1-{{\tan }^{2}}B}
\end{align}$
Hence, the required value of tan 2B is $\frac{2\tan \,B}{1-{{\tan }^{2}}B}$.
