如果 $\sin x+\cos x=\frac{1}{5}$, 且 $0<x<\pi$, 那么 $\tan x$ 的值是 ( )
将所给等式两边平方, 得 $\sin x \cos x=-\frac{12}{25}$,

$\because 0<x<\pi, \therefore \sin x>0, \cos x<0$, $(\sin x-\cos x)^{2}=1-2 \sin x \cos x=\frac{49}{25}$,

$\therefore \sin x-\cos x=\frac{9}{5}, \therefore \sin x=\frac{4}{5}, \cos x=-\frac{3}{5}, \therefore \tan x=-\frac{4}{3}$, 故选 A.