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જો $\alpha$, $\beta$,$\gamma$ એ ધન સંખ્યાઓ છે કે જેથી $\alpha + \beta = \pi$ અને $\beta + \gamma = \alpha$ થાય તો $tan\ \alpha$= ................ (જ્યાં $\gamma \ne n\pi ,n \in I$ )
$ - 2\sqrt {\frac{{\tan \beta + \tan \gamma }}{{\tan \gamma }}}$
$\sqrt {\frac{{2\tan \beta + \tan \gamma }}{{\tan \gamma }}}$
$ - \sqrt {\frac{{2\tan \beta + \tan \gamma }}{{\tan \gamma }}}$
$\sqrt {\frac{{\tan \beta + \tan \gamma }}{{\tan \gamma }}}$
Solution
$\beta+\gamma=\alpha$
$\frac{\tan \beta+\tan \gamma}{1-\tan \beta \tan \gamma}=\tan \alpha$
$\tan \beta+\tan \gamma=\tan \alpha-\tan \beta \tan \gamma \tan \alpha$
use $\alpha+\beta=\pi \,\,\,and\,\,\,\,\,$$ \beta+r= \alpha$
$\tan \beta+\tan \gamma=-\tan \beta+\tan ^{2} \alpha \tan \gamma$
$\tan ^{2} \alpha=\frac{2 \tan \beta+\tan \gamma}{\tan \gamma}$
$\tan \alpha=-\sqrt{\frac{2 \tan \beta+\tan \gamma}{\tan \gamma}}$
