Task B-3.3. Determine the fundamental period of the function $f(x)=8 \sin ^{2} x \cos ^{2} x-2 \cos ^{2} 2 x$.
Solution. Let's write the function $f$ as

$$
f(x)=2(2 \sin x \cos x)^{2}-2 \cos ^{2} 2 x=2 \sin ^{2} 2 x-2 \cos ^{2} 2 x=-2 \cos 4 x
$$

The fundamental period of this function is $\frac{2 \pi}{4}=\frac{\pi}{2}$.