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

The value of ,$\sqrt 3 \, cosec\, 20^o - sec\, 20^o $ is :

If $A$ and $B$ are complimentary angles, then :

$\cos A + \cos (240^\circ + A) + \cos (240^\circ - A) = $

$1 + \cos \,{56^o} + \cos \,{58^o} - \cos {66^o} = $

If $\tan \alpha = \frac{1}{7}$ and $\sin \beta = \frac{1}{{\sqrt {10} }}\left( {0 < \alpha ,\,\beta < \frac{\pi }{2}} \right)$, then $2\beta $ is equal to