1. Let $a, b, c$ be real numbers. Then for any real number $x$, the inequality $a \sin x + b \cos x + c > 0$ always holds if and only if
(A) $a, b$ are both 0, and $c > 0$
(B) $\sqrt{a^{2}+b^{2}} = c$
(C) $\sqrt{a^{2}+b^{2}} < c$
(C)
I. Multiple Choice Question
1. 【Analysis and Solution】When $a, b$ are not both zero,
$$
\begin{array}{l}
a \sin x+b \cos x+c>0 \\
\Leftrightarrow \sqrt{a^{2}+b^{2}} \sin (x+\varphi)+c>0 \\
\Leftrightarrow \sin (x+\varphi)>-\frac{c}{\sqrt{a^{2}+b^{2}}}
\end{array}
$$

For (2) to hold, the necessary and sufficient condition is $-\frac{c}{\sqrt{a^{2}+b^{2}}}\sqrt{a^{2}+b^{2}}$, which is included in (C). Therefore, the answer is (C).