$-x^2 \le x^2 \cos\left(\frac{1}{x^2}\right) \le x^2$

$-1 \le x^2 \cos\left(\frac{1}{x^2}\right) \le 1$

$-\frac{1}{x^2} \le x^2 \cos\left(\frac{1}{x^2}\right) \le \frac{1}{x^2}$

$-x^2 \le \cos\left(\frac{1}{x^2}\right) \le x^2$