Evaluate the following:
$2 \tan ^{2} 45^{\circ}+\cos ^{2} 30^{\circ}-\sin ^{2} 60^{\circ}$

$\sin 60^{\circ} \cdot \cos 30^{\circ} + \cos 60^{\circ} \cdot \sin 30^{\circ} = ..........$

If $\cos \theta = \frac{1}{\sqrt{2}},$ then $\theta = \ldots$ (in $^\circ$)

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

In a right triangle,if the measure of one of the angles is $60^{\circ}$,then the measure of the side opposite to the angle with measure $60^{\circ}$ is $\ldots \ldots$ times the measure of the hypotenuse.

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