已知函数 $f(x)=\ln \left(\sqrt{\sin ^2 x+1}+\sin x\right)(x \in R)$ ，则存在非零实数 $x_0$ ，使得
A. $f\left(x_0\right)=-1$
B. $f\left(x_0\right)-f\left(-x_0\right)=2$
C. $f\left(f\left(x_0\right)\right)=\ln (\sqrt{2}+1)$
D. $f\left(\pi+x_0\right)-f\left(x_0\right)=\frac{3}{2}$