2. Where do the functions $f(x)=\sin 4 x$ and $g(x)=-\cos 2 x$ have the same value?
2. Writing $f(x)=g(x)$ or $\sin 4 x=-\cos 2 x$ ..... 0.5 points
$2 \sin 2 x \cos 2 x+\cos 2 x=0$ ..... 1 point
Writing in product form: $\cos 2 x(2 \sin 2 x+1)=0$ ..... 1 point
Writing equations: $\cos 2 x=0$ ..... 0.5 points
$\sin 2 x=-\frac{1}{2}$ ..... 0.5 points
Solution: $x_{1}=\frac{\pi}{4}+\frac{k \pi}{2}$ ..... 1 point
$x_{2}=-\frac{\pi}{12}+k \pi$ ..... 1 point
$x_{3}=\frac{7 \pi}{12}+k \pi, k \in \mathbf{Z}$ ..... 0.5 points
Note: If the result is given without the period, subtract 0.5 points.