Cho tanα=−2. Tính P=sinα−cosα/sin3α+3cos3α+2sinα.

Chọn A

\(P = \frac{{\sin \alpha - \cos \alpha }}{{{{\sin }^3}\alpha + 3{{\cos }^3}\alpha + 2\sin \alpha }} = \frac{{\tan \alpha \frac{1}{{co{s^2}\alpha }} - \frac{1}{{co{s^2}\alpha }}}}{{{{\tan }^3}\alpha + 3 + 2\tan \alpha \frac{1}{{co{s^2}\alpha }}}} = \frac{{\left( {\tan \alpha - 1} \right)\left( {1 + {{\tan }^2}\alpha } \right)}}{{{{\tan }^3}\alpha + 3 + 2\tan \alpha \left( {1 + {{\tan }^2}\alpha } \right)}} = \frac{3}{5}\)