If $A = 30^{\circ}$,then the value of $\cos 2A$ is $\ldots \ldots \ldots . .$

For acute angles $A$ and $B,$ if $\tan A = 1$ and $\sin B = \frac{1}{\sqrt{2}},$ then $\cos (A + B) = \dots$

If $\sec \theta = 1$,then $\theta = \ldots \ldots \ldots$ (in $^{\circ}$)

In a right triangle,if the measure of one of the angles is $45^{\circ}$,then the measure of the side opposite to the angle with measure $45^{\circ}$ is $\ldots \ldots \ldots$ times the measure of the hypotenuse.

Evaluate the following:
$\frac{5 \cos ^{2} 60^{\circ}+4 \sec ^{2} 30^{\circ}-\tan ^{2} 45^{\circ}}{\sin ^{2} 30^{\circ}+\cos ^{2} 30^{\circ}}$ (in $/12$)

If $\tan (A + B) = \sqrt{3}$ and $\tan (A - B) = \frac{1}{\sqrt{3}}$,where $0^{\circ} < A + B \leq 90^{\circ}$ and $A > B$,find the values of $A$ and $B$.