4. Given $\alpha, \beta, \alpha+\beta \in\left(0, \frac{\pi}{2}\right)$,
$$
A=\frac{1}{\sin 2 \alpha}+\frac{1}{\sin 2 \beta}, B=\frac{1}{\sin \alpha}+\frac{1}{\sin \beta} \text {. }
$$

Then ( ).
(A) $AB$
(D) $A \geqslant B$
4.A.

From $\alpha, \beta, \alpha+\beta \in \left(0, \frac{\pi}{2}\right)$, we get
$$
\begin{array}{l}
\sin (\alpha+\beta)=\sin \alpha \cdot \cos \beta+\cos \alpha \cdot \sin \beta \\
\frac{\sin (\alpha+\beta)}{\sin \alpha \cdot \sin \beta}-\frac{2 \sin (\alpha+\beta) \cdot \cos (\alpha-\beta)}{\sin 2 \alpha \cdot \sin 2 \beta} \\
=\frac{2 \sin (\alpha+\beta)[2 \cos \alpha \cdot \cos \beta-\cos (\alpha-\beta)]}{\sin 2 \alpha \cdot \sin 2 \beta} \\
=\frac{2 \sin (\alpha+\beta) \cdot \cos (\alpha+\beta)}{\sin 2 \alpha \cdot \sin 2 \beta}>0 .
\end{array}
$$