Cho $ \alpha +\beta ={{90}^{0}}$ . Tính $ A=\sin \alpha . \cos \beta +\cos \alpha . \sin \beta +\cos \alpha . \cos \beta -\sin \alpha . \sin \be

Cho $ \alpha +\beta ={{90}^{0}}$ . Tính $ A=\sin \alpha . \cos \beta +\cos \alpha . \sin \beta +\cos \alpha . \cos \beta -\sin \alpha . \sin \beta $
A. $ 4. $
B. $ 3. $
C. $ 2. $
D. $ 1. $

$ \alpha +\beta ={{90}^{0}}\Rightarrow \left\{ \begin{array}{l}
\sin \alpha =\cos \beta
\\
\cos \alpha =\sin \beta
\end{array} \right. $
$ A=\sin \alpha . \cos \beta +\cos \alpha . \sin \beta +\cos \alpha . \cos \beta -\sin \alpha . \sin \beta $
$ ={{\sin }^{2}}\alpha +{{\cos }^{2}}\alpha +\sin \alpha . \cos \alpha -\sin \alpha . \cos \alpha =1. $ Chọn đáp án D.