1. When $0<x \leqslant 1$, which of the following inequalities is correct? ( ).
(A) $\frac{\sin x}{x}<\left(\frac{\sin x}{x}\right)^{2} \leqslant \frac{\sin x^{2}}{x^{2}}$
(B) $\left(\frac{\sin x}{x}\right)^{2}<\frac{\sin x}{x} \leqslant \frac{\sin x^{2}}{x^{2}}$
(C) $\left(\frac{\sin x}{x}\right)^{2}<\frac{\sin \frac{x^{2}}{x^{2}} \leqslant \frac{\sin }{x} \cdot x}{x}$
(D) $\frac{\sin x^{2}}{x^{2}} \leqslant\left(\frac{\sin x}{x}\right)^{2}<\frac{\sin x}{x}$
-1 (B).
Because $0\left(\frac{\sin x}{x}\right)^{2}$. Also, since $f(x) = \frac{\sin x}{x}$ is a decreasing function on $\left(0, \frac{\pi}{2}\right)$, and $0 < x^{2} \leqslant x \leqslant 1 < \frac{\pi}{2}$, it follows that $\frac{\sin x^{2}}{x^{2}} \geqslant \frac{\sin x}{x}$.