Biết (cos α + sin 2 α )/(1 + sin α − cos 2 α )= x . tan α + y . cot α ( x , y ∈ R ) . Tính S = x − y

Chọn A

\(\begin{array}{l}\frac{{\cos \alpha  + \sin 2\alpha }}{{1 + \sin \alpha  - \cos 2\alpha }} = \frac{{\cos \alpha  + 2\sin \alpha \cos \alpha }}{{1 + \sin \alpha  - \left( {1 - 2{\rm{si}}{{\rm{n}}^2}\alpha } \right)}} = \frac{{\cos \alpha \left( {1 + 2\sin \alpha } \right)}}{{\sin \alpha \left( {1 + 2\sin \alpha } \right)}}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \cot \alpha  = 0.\tan \alpha  + 1.\cot \alpha  = x.\tan \alpha  + y.\cot \alpha \,\\\,\,\, \Rightarrow \left\{ \begin{array}{l}x = 0\\y = 1\end{array} \right.\end{array}\)

\(S = x - y = 0 - 1 =  - 1\)