In $\triangle ABC$, $A>B$ is a condition for $\cos 2B > \cos 2A$ to be
A. sufficient but not necessary
B. necessary but not sufficient
C. both sufficient and necessary
D. neither sufficient nor necessary

保留源文本的换行和格式，翻译结果如下：

In $\triangle ABC$, $A>B$ is a condition for $\cos 2B > \cos 2A$ to be
A. sufficient but not necessary
B. necessary but not sufficient
C. both sufficient and necessary
D. neither sufficient nor necessary
86 C. In $\triangle A B C$,
$$
\begin{aligned}
A>B & \Leftrightarrow a>b \\
& \Leftrightarrow 2 R \sin A>2 R \sin B \\
& \Leftrightarrow \sin A>\sin B>0 \\
& \Leftrightarrow \sin ^{2} A>\sin ^{2} B \\
& \Leftrightarrow 1-2 \sin ^{2} B>1-2 \sin ^{2} A \\
& \Leftrightarrow \cos 2 B>\cos 2 A .
\end{aligned}
$$