设 $\alpha,\beta\in(0,\frac{\pi}{2})$, 且 $\alpha\neq\beta$, 证明: $1 < \frac{\alpha\cos\beta-\beta\cos\alpha}{\alpha-\beta} < \frac{\pi}{2}$.
设 $\alpha,\beta\in(0,\frac{\pi}{2})$, 且 $\alpha\neq\beta$, 证明:
\[1 < \frac{\alpha\cos\beta-\beta\cos\alpha}{\alpha-\beta} < \frac{\pi}{2}.\]