Let $\alpha ,\beta$ and $\gamma$ be some angles in the first quadrant satisfying $\tan \left(\alpha +\beta \right)=\frac{15}{8}$ and $\cos ec\gamma =\frac{17}{8}$ , then which of the following hold(s) good ?

$\tan \left(\alpha +\beta \right)=\frac{15}{8}\Rightarrow \tan \left(\alpha +\beta \right)\tan y=1$

$\Rightarrow 1-\tan \left(\alpha +\beta \right).\tan \gamma =0$

$\Rightarrow \frac{1}{1-\tan \left(\alpha +\beta \right).\tan \gamma }=\infty$

$\Rightarrow \frac{\tan \left(\alpha +\beta \right)+\tan \gamma }{1-\tan \left(\alpha +\beta \right).\tan \gamma }=\tan \frac{\pi }{2}$

$\Rightarrow \tan \left(\alpha +\beta +\gamma \right)=\tan \frac{\pi }{2}$

$\Rightarrow \alpha +\beta +\gamma =\frac{\pi }{2}$

$\Rightarrow \tan \left(\alpha +\beta \right)=\frac{\tan \alpha +\tan \beta }{1-\tan \alpha .\tan \beta }$

$\frac{1}{\tan y}=\frac{\tan \alpha +\tan \beta }{1-\tan \alpha .\tan \beta }$

$\Rightarrow 1-\tan \alpha +\tan \beta =\tan \alpha .\tan y+\tan \beta +\tan \gamma$

$\Rightarrow \tan \alpha \tan \beta +\tan \beta \tan \gamma +\tan \gamma .\tan \alpha =1$