## Task B-3.3.

Determine the maximum and minimum value of the function

$$
f(x)=\sqrt{\sin ^{4} x+4 \cos ^{2} x}-\sqrt{\cos ^{4} x+4 \sin ^{2} x}
$$
## Solution.

$$
\begin{aligned}
f(x) & =\sqrt{\left(1-\cos ^{2} x\right)^{2}+4 \cos ^{2} x}-\sqrt{\left(1-\sin ^{2} x\right)^{2}+4 \sin ^{2} x}= & & 1 \text { point } \\
& =\sqrt{\cos ^{4} x+2 \cos ^{2} x+1}-\sqrt{\sin ^{4} x+2 \sin ^{2} x+1}= & & 1 \text { point } \\
& =\sqrt{\left(1+\cos ^{2} x\right)^{2}}-\sqrt{\left(1+\sin ^{2} x\right)^{2}}= & & 1 \text { point } \\
& =1+\cos ^{2} x-1-\sin ^{2} x=\cos 2 x . & & 1 \text { point }
\end{aligned}
$$

The maximum value of the function $f$ is 1, and the minimum value is -1.