1. Given $x=\frac{\pi}{12}$, then the value of the function $f(x)=$ $\sqrt{\sin ^{4} x+4 \cos ^{2} x}-\sqrt{\cos ^{4} x+4 \sin ^{2} x}$ is $\qquad$ .
$$
\begin{array}{l}
\text { 1. } \frac{\sqrt{3}}{2} . \\
\text { Solution: } \because \text { Original expression }=\sqrt{\left(\sin ^{2} x-2\right)^{2}}-\sqrt{\left(\cos ^{2} x-2\right)^{2}} \\
=\cos ^{2} x-\sin ^{2} x=\cos 2 x . \\
\quad \therefore \text { when } x=\frac{\pi}{12}, \text { the original expression }=\frac{\sqrt{3}}{2} .
\end{array}
$$
1. $\frac{\sqrt{3}}{2}$.

Solution: $\because$ Original expression $=\sqrt{\left(\sin ^{2} x-2\right)^{2}}-\sqrt{\left(\cos ^{2} x-2\right)^{2}}$ $=\cos ^{2} x-\sin ^{2} x=\cos 2 x$.
$\therefore$ when $x=\frac{\pi}{12}$, the original expression $=\frac{\sqrt{3}}{2}$.