Ta có: $tanA = 2$
$\Rightarrow cotA = \dfrac{1}{2}$
$\Rightarrow tanA + cotA = \dfrac{5}{2}$
$\Leftrightarrow \dfrac{1}{sinAcosA} = \dfrac{5}{2}$
$\Leftrightarrow sinAcosA = \dfrac{2}{5}$
$\Leftrightarrow sinA = \dfrac{2}{5cosA}$
Ta lại có: $sin^2A + cos^2A = 1$
$\Rightarrow \dfrac{4}{25cos^2A} + cos^2A = 1$
$\Leftrightarrow 25cos^4A - 25cos^2A + 4 = 0$
$\Leftrightarrow \left[\begin{array}{l}cosA = \pm \dfrac{2}{\sqrt5}\\cosA = \pm \dfrac{1}{\sqrt5}\end{array}\right.$
$\Leftrightarrow \left[\begin{array}{l}sinA = \pm \dfrac{1}{\sqrt5}\\sinA = \pm \dfrac{2}{\sqrt5}\end{array}\right.$
