6. (9th "Hope Cup" Senior High School Competition) Let $T_{1}, T_{2}, T_{3}$ represent the smallest positive periods of the functions $\tan \frac{x}{\sqrt{2}}, |\cos x|$, $\sin \frac{x}{3}\left(\sin \frac{x}{3}+\cos \frac{x}{3}\right)$, respectively. Then
A. $T_{1}<T_{2}<T_{3}$
B. $T_{3}<T_{2}<T_{1}$
C. $T_{2}<T_{1}<T_{3}$
D. $T_{2}<T_{3}<T_{1}$
6. C It is easy to know that $T_{1}=\frac{\pi}{\frac{1}{\sqrt{2}}}=\sqrt{2} \pi, T_{2}=\pi$, now we find $T_{3}$:

Since
$$
\begin{aligned}
\sin \frac{x}{3}\left(\sin \frac{x}{3}+\cos \frac{x}{3}\right) & =\sin ^{2} \frac{2 x}{3}+\frac{1}{2} \sin \frac{2 x}{3} \\
& =\frac{1-\cos \frac{2 x}{3}}{2}+\frac{1}{2} \sin \frac{2 x}{3}=\frac{1}{2}+\frac{\sqrt{2}}{2} \sin \left(\frac{2 x}{3}-\frac{\pi}{4}\right),
\end{aligned}
$$

so $T_{3}=\frac{2 \pi}{\frac{2}{3}}=3 \pi, T_{2}<T_{1}<T_{3}$, choose $\mathrm{C}$.