Which one of the following is true?

If $A = \sin 45^{\circ} + \cos 45^{\circ}$ and $B = \sin 44^{\circ} + \cos 44^{\circ}$,then

If $\sin A = \frac{1}{\sqrt{10}}$ and $\sin B = \frac{1}{\sqrt{5}}$,where $A$ and $B$ are positive acute angles,then $A + B = $

$\sin 20^\circ \sin 40^\circ \sin 60^\circ \sin 80^\circ = $ (in $/16$)

If $\alpha, \beta, \gamma \in \left( 0, \frac{\pi}{2} \right)$,then $\frac{\sin(\alpha + \beta + \gamma)}{\sin \alpha + \sin \beta + \sin \gamma}$ is

If $a \tan \theta = b$,then $a \cos 2\theta + b \sin 2\theta = $