3. In $\triangle A B C$, $\cos 2 B>\cos 2 A$ is a ( ) for $A>B$.
(A) sufficient but not necessary condition
(B) necessary but not sufficient condition
(C) sufficient and necessary condition
(D) neither sufficient nor necessary condition
3. (C).
$$
\begin{array}{l}
\therefore \text { In } \triangle A B C, A>B \Leftrightarrow a>b \Leftrightarrow 2 R \sin A>2 R \sin B \\
\Leftrightarrow \sin A>\sin B>0 \Leftrightarrow \sin ^{2} A>\sin ^{2} B \Leftrightarrow-2 \sin ^{2} A1-2 \sin ^{2} A \Leftrightarrow \cos 2 B>\cos 2 A .
\end{array}
$$