Cho sin α + cos β = 5/ 4 , khi đó sin 2 α có giá trị bằng:

C

Ta có:\[\sin \alpha  + \cos \beta  = \frac{5}{4} \Leftrightarrow {\left( {\sin \alpha  + \cos \beta } \right)^2} = {\left( {\frac{5}{4}} \right)^2} = \frac{{25}}{{16}}\]

\[ \Rightarrow {\sin ^2}\alpha  + 2\sin \alpha \cos \beta  + {\cos ^2}\beta  = \frac{{25}}{{16}}\]

\[ \Rightarrow 1 + \sin 2\alpha  = \frac{{25}}{{16}}\]

\[ \Rightarrow \sin 2\alpha  = \frac{{25}}{{16}} - 1 = \frac{9}{{16}}\].