If $\alpha$, $\beta$,$\gamma$ are positive number such that $\alpha + \beta = \pi$  and $\beta  + \gamma = \alpha$, then $tan\ \alpha$ is equal to - (where $\gamma  \ne n\pi ,n \in I$ )

  • A

    $ - 2\sqrt {\frac{{\tan \beta  + \tan \gamma }}{{\tan \gamma }}}$

  • B

    $\sqrt {\frac{{2\tan \beta  + \tan \gamma }}{{\tan \gamma }}}$

  • C

    $ - \sqrt {\frac{{2\tan \beta  + \tan \gamma }}{{\tan \gamma }}}$

  • D

    $\sqrt {\frac{{\tan \beta  + \tan \gamma }}{{\tan \gamma }}}$

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