16. The maximum value of the function $f(x)=\frac{2 \sin x \cos x}{1+\sin x+\cos x}$ is $\qquad$
II. 16. Since $f(x)=\frac{(\sin x+\cos x)^{2}-1}{1+\sin x+\cos x}=\sin x+\cos x-1=\sqrt{2} \sin \left(x+\frac{\pi}{4}\right)-1$, therefore, $f(x)$ has a maximum value of $\sqrt{2}-1$