Example 4, $\sin x + \cos x > 1$, find the range of values for $x$.

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Let $\operatorname{tg} \frac{x}{2}=\mathrm{t}$, substitute into the inequality to solve for $0<t<1$, thus $2 k \pi<x<2 k \pi+\frac{\pi}{2}, k \in Z$.

