If ${{\sqrt 2 \sin \alpha } \over {\sqrt {1 + \cos 2\alpha } }} = {1 \over 7}$ and $\sqrt {{{1 - \cos 2\beta } \over 2}} = {1 \over {\sqrt {10} }}$ $\alpha ,\beta \in \left( {0,{\pi \over 2}} \right)$ then tan($\alpha $ + 2$\beta $) is equal to _____.

Question

If ${{\sqrt 2 \sin \alpha } \over {\sqrt {1 + \cos 2\alpha } }} = {1 \over 7}$ and $\sqrt {{{1 - \cos 2\beta } \over 2}} = {1 \over {\sqrt {10} }}$

$\alpha ,\beta \in \left( {0,{\pi \over 2}} \right)$ then tan($\alpha $ + 2$\beta $) is equal to _____.

Correct Answer

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