The value of $\sin^{2} 30^{\circ} - \tan 45^{\circ} + \cos^{2} 60^{\circ} - \cot 90^{\circ}$ is ........

If $\sin ( A - B ) = \frac{1}{2}$,$\cos ( A + B ) = \frac{1}{2}$,$0^{\circ} < A + B \leq 90^{\circ}$,and $A > B$,find $A$ and $B$.

$\frac{2 \tan 30^{\circ}}{1-\tan ^{2} 30^{\circ}} = ?$

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.

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 $B$.

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