Cho \(\tan a = 2\) tính giá trị \(A = \dfrac{1}{{{{\cos }^2}a}} + \dfrac{{\cos a + \sin a}}{{\cos a - \sin a}} - 5\)

* Hướng dẫn giải

Vì \(\tan \alpha  = 2 \Rightarrow \cos \alpha  \ne 0\), ta có:

\(A = \dfrac{1}{{{{\cos }^2}a}} + \dfrac{{\cos a + \sin a}}{{\cos a - \sin a}} - 5\)

\( = 1 + {\tan ^2}\alpha  + \dfrac{{\dfrac{{\cos \alpha }}{{\cos \alpha }} + \dfrac{{\sin \alpha }}{{\cos \alpha }}}}{{\dfrac{{\cos \alpha }}{{\cos \alpha }} - \dfrac{{\sin \alpha }}{{\cos \alpha }}}} - 5\)

\( = 1 + {\tan ^2}\alpha  + \dfrac{{1 + \tan \alpha }}{{1 - \tan \alpha }} - 5\)

\( = 1 + {2^2} + \dfrac{{1 + 2}}{{1 - 2}} - 5 =  - 3\)

Chọn C