3. $\log _{\sin 1} \cos 1, \log _{\sin 1} \tan 1, \log _{\operatorname{cos1}} \sin 1$, from largest to smallest is
3. $\log _{\sin 1} \cos 1>\log _{\cos 1} \sin 1>\log _{\sin 1} \tan 1$.

Given $\frac{\pi}{4}<1<\frac{\pi}{2}$, we have $0<\cos 1<\sin 1<1$,
$$
\begin{array}{l}
\log _{\cos 1} \sin 1>0 \text{. Also, } \log _{\cos 1} \sin 1 \\
\log _{\cos 1} \sin 1>\log _{\sin 1} \tan 1 .
\end{array}
$$