4. Given $0<b<1,0<\alpha<\frac{\pi}{4}$, then the size relationship of the following three numbers: $x=(\sin \alpha)^{\log _{b} \sin \alpha}, y=(\cos \alpha)^{\log _{b} \cos \alpha}$, $z=(\sin \alpha)^{\log _{b} \cos \alpha}$ is
A. $x<z<y$
B. $y<z<x$
C. $z<x<y$
D. $x<y<z$
Solve:
$$
0\log _{b} \cos \alpha>0
$$
$\Rightarrow(\sin \alpha)^{\log _{b} \sin \alpha}<(\sin \alpha)^{\log _{b} \cos \alpha}<(\cos \alpha)^{\log _{b} \cos \alpha} \Rightarrow x<z<y$, so the answer is $A$.