9. If $x, y \in[0, \pi]$, for any real number $t$, the expression $\left(-2 \cos t-\frac{1}{2} \cos x \cos y\right) \cos x \cos y-1$ $-\cos x+\cos y-\cos 2 t$ is always negative, find the relationship that $x, y$ must satisfy.
9. Solution: The original expression can be transformed into: $2\left(\cos t+\frac{\cos x \cos y}{2}\right)^{2}+\cos x-\cos y>0$ for any real number $t$.

Since $\left(\cos t+\frac{\cos x \cos y}{2}\right)^{2} \geqslant 0$, it follows that $\cos x-\cos y>0$, which means $0 \leqslant x<y \leqslant \pi$.