4. Let $\alpha, \beta, \gamma \in\left(0, \frac{\pi}{2}\right)$, and $\cot \alpha=\alpha, \sin (\operatorname{col} \beta)=\beta, \cot (\sin \gamma)=\gamma$, then the size relationship of $\alpha$, $\beta, \gamma$ is ( ).
A. $\alpha<\beta<7$
B. $\alpha<\gamma<\beta$
C. $\gamma<\beta<\alpha$
D. $\beta<a<\gamma$
4. D

As shown in the figure, since $\cot \alpha=\alpha, \alpha \in\left(0, \frac{\pi}{2}\right)$, then for the two functions $f(x)=\cot x\left(00)$, we get $\beta=$ $\sin (\cot \beta)g(\beta)$, combining with the graph we know $\beta \in(0, \alpha)$.
Since the function $y=\cot \alpha$ is decreasing in $\left(0, \frac{\pi}{2}\right)$, and $0\cot \gamma$, i.e., $f(\gamma)<g(\gamma)$, from the graph we know $\gamma \in\left(\alpha, \frac{\pi}{2}\right)$. In summary, we have: $\beta<\alpha<\gamma$, hence the answer is $\mathrm{D}$.