1. Let $a, b, c$ be real numbers. Then, for any real number $x$, the necessary and sufficient condition for the inequality $a \sin x+b \cos x+c>0$ to always hold is
A. $a, b$ are both 0, and $c>0$
B. $\sqrt{a^{2}+b^{2}}=c$
C. $\sqrt{a^{2}+b^{2}}c$
Solve:
$a \sin x + b \cos x + c = \sqrt{a^{2} + b^{2}} \sin (x + \theta) + c > 0$ always holds $\Rightarrow -\sqrt{a^{2} + b^{2}} + c > 0$ $\Rightarrow \sqrt{a^{2} + b^{2}} < c$. Therefore, choose $C$.