$$\frac{1-\sin \theta+\cos \theta}{1-\sin \theta-\cos \theta}=$$

If $A$ and $B$ are supplementary angles, then $\sin ^2 \frac{A}{2}+\sin ^2 \frac{B}{2}=$

$$\begin{aligned} & \cos \left(36^{\circ}-A\right) \cos \left(36^{\circ}+A\right)+\cos \left(54^{\circ}+A\right) \cos \\ & \left(54^{\circ}-A\right)= \end{aligned}$$

If $$x+y=\frac{\pi}{2}$$, then the maximum value of $$\sin x \cdot \sin y$$ is