a) cos α > 0 .

\({\rm{V\`i  }}\frac{\pi }{2} < \alpha  < \pi {\rm{ n\^e n }}\cos \alpha  < 0.{\rm{ }}\)

Ta có \({\cos ^2}\alpha  = 1 - {\sin ^2}\alpha  = 1 - \frac{1}{4} = \frac{3}{4} \Rightarrow \cos \alpha  =  - \frac{{\sqrt 3 }}{2}\) (vì\(\cos \alpha  < 0\)).

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

\(\cos 2\alpha  = 1 - 2{\sin ^2}\alpha  = 1 - 2 \cdot {\left( {\frac{1}{2}} \right)^2} = \frac{1}{2}\). Suy ra \(\cos 2\alpha  = \sin \alpha \).

Đáp án:           a) Sai,             b) Sai,             c) Đúng,          d) Đúng.