3. The trajectory of the moving point in the complex plane
$$
Z\left(\frac{\cos \theta+\sin \theta}{1+\cos \theta \cdot \sin \theta}, \frac{\cos \theta \cdot \sin \theta}{1+\cos \theta \cdot \sin \theta}\right)(\theta \in \mathbf{R})
$$

is ( ).
(A) Circle
(B) Ellipse
(C) Hyperbola
(D) Parabola
$\begin{array}{l}\text { 3. A. } \\ =\left(\frac{\cos \theta+\sin \theta}{1+\cos \theta \cdot \sin \theta}\right)^{2}+\left(\frac{\cos \theta \cdot \sin \theta}{1+\cos \theta \cdot \sin \theta}\right)^{2} \\ =1\end{array}$

The translation is as follows:

$\begin{array}{l}\text { 3. A. } \\ =\left(\frac{\cos \theta+\sin \theta}{1+\cos \theta \cdot \sin \theta}\right)^{2}+\left(\frac{\cos \theta \cdot \sin \theta}{1+\cos \theta \cdot \sin \theta}\right)^{2} \\ =1\end{array}$