2. Given $0<\alpha<\frac{\pi}{2}, 0<\beta<\frac{\pi}{2}$, and $\sin \frac{\alpha}{2}$ $=a \cos \beta$. When $0<\alpha+\beta<\frac{\pi}{2}$, the range of values for $a$ is $\qquad$.
2. $0<a \leqslant \frac{1}{2}$.