1. Given the function
$$
f(x)=\sqrt{\sin ^{4} x+4 \cos ^{2} x}-\sqrt{\cos ^{4} x+4 \sin ^{2} x} .
$$

Then $f(x)$ can be simplified to (.
(A) $\cos 2 x$
(B) $\sin 2 x$
(C) $\cos x-\sin x$
(D) $\cos \frac{x}{2}-\sin \frac{x}{2}$
$-、 1 . A$
Since $\sin ^{4} x+4 \cos ^{2} x=\left(\sin ^{2} x-2\right)^{2}$, therefore,
$$
\sqrt{\sin ^{4} x+4 \cos ^{2} x}=2-\sin ^{2} x \text {. }
$$

Similarly, $\sqrt{\cos ^{4} x+4 \sin ^{2} x}=2-\cos ^{2} x$.
Thus, $f(x)=\cos ^{2} x-\sin ^{2} x=\cos 2 x$.