Khi đó A = tan α − cot α bằng

Ta có \(\cos \alpha = \pm \sqrt {1 - {{\sin }^2}\alpha } = \pm \sqrt {1 - {{\left( {\frac{2}{3}} \right)}^2}} = \pm \frac{{\sqrt 5 }}{3}\).

Do \(0 \le \alpha \le \frac{\pi }{2}\) nên \(\cos \alpha = \frac{{\sqrt 5 }}{3}\).

Suy ra \(A = \tan \alpha - \cot \alpha = \frac{{\sin \alpha }}{{\cos \alpha }} - \frac{{\cos \alpha }}{{\sin \alpha }} = \frac{{\frac{2}{3}}}{{\frac{{\sqrt 5 }}{3}}} - \frac{{\frac{{\sqrt 5 }}{3}}}{{\frac{2}{3}}} = - \frac{{\sqrt 5 }}{{10}}\). Chọn D.