Cho biết cos α = − 2/3 . Tính tan α ?

Chọn D

Ta có \(1\, + \,\,{\tan ^2}\alpha \,\, = \,\,\frac{1}{{{\rm{co}}{{\rm{s}}^2}\alpha }}\,\, \Rightarrow \,\,{\tan ^2}\alpha \,\, = \,\,\frac{1}{{{{\left( { - \frac{2}{3}} \right)}^2}}}\,\, - \,\,1\,\, = \,\,\frac{5}{4}\).

Suy ra \(\tan \alpha \,\, = \,\, - \frac{{\sqrt 5 }}{2}\) (vì \(\cos \alpha \, < \,\,0\, \Rightarrow \,\,\tan \alpha \,\, < \,\,0\)).