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.