4. Given $f(x)=\frac{\sin x}{2+\cos x}$, then for $\forall x \in \mathbf{R}$, which of the following statements is incorrect?
A: $\quad f(x) \geq \frac{1}{3} \sin x$
B: $\quad|f(x)| \leq|x|$
C: $|f(x)| \leq \frac{\sqrt{3}}{3}$
D: $\quad f(\pi+x)+f(\pi-x)=0$
Answer A.
Hint $\quad|f(x)|=\frac{|\sin x|}{|2+\cos x|} \leq|\sin x| \leq|x|$.