Cho sin α = 2/3 ( 0 ∘ < α < 90 ∘ ) . Khi đó: a) cos α < 0

Vì \({\sin ^2}\alpha  + {\cos ^2}\alpha  = 1 \Rightarrow {\cos ^2}\alpha  = 1 - {\sin ^2}\alpha  = 1 - {\left( {\frac{2}{3}} \right)^2} = \frac{5}{9}\).

Mà 0°<α<90° nên \(\cos \alpha  > 0\). Do đó \(\cos \alpha  = \frac{{\sqrt 5 }}{3}\) nên\(A = \frac{{\sin \alpha  + \sqrt 5 \cos \alpha }}{{2\sin \alpha  + \cos \alpha }} = \frac{7}{{4 + \sqrt 5 }}\).