$\color{red}{(} \color{#FF5500}{っ} \color{#FFAA00}{◔} \color{#FFFF00}{◡} \color{#AAFF00}{◔} \color{#55FF00}{)} \color{#00FF00}{っ} \color{#00FF55}{ ♥} \color{#00FFAA}{n} \color{#00FFFF}{h} \color{#00AAFF}{i} \color{#0055FF}{x}\color{#0000FF}{i} \color{#5500FF}{n} \color{#AA00FF}{h} \color{#FF00FF}{i} \color{#FF00AA}{u} \color{#FF0055}{♥} $

Ta có: `\pi/2 < \alpha < \pi`

`\Rightarrow \alpha` thuộc góc phần tư thứ II

Biết: `sin\alpha +cos\alpha = 1/5`

`(sin\alpha +cos\alpha).1/cos\alpha =1/5 .1/cos\alpha`

`tan\alpha +1 = 1/5  .1/cos\alpha`

`(tan\alpha +1)^2=(1/5 .1/cos\alpha)^2`

`tan^2\alpha +2tan\alpha +1=1/25 . (1+tan^2\alpha)`

`tan^2\alpha +2tan\alpha +1 =1/25 + 1/25 tan^2\alpha`

`24/25 tan^2\alpha +2tan\alpha +24/25=0`

`\Rightarrow`\(\left[ \begin{array}{l}tan\alpha=-\frac{3}{4}\\tan\alpha=\frac{-4}{3}\end{array} \right.\)