(4) In $\triangle A B C$, “$A\cos 2 B>\cos 2 C$” is
(A) a sufficient but not necessary condition
(B) a necessary but not sufficient condition
(C) a sufficient and necessary condition
(D) neither a sufficient nor a necessary condition
(C)
Solution: (C)
$$
\begin{array}{l}
A1-2 \sin ^{2} B>1-2 \sin ^{2} C \Leftrightarrow \cos 2 A>\cos 2 B>\cos 2 C .
\end{array}
$$