JEE Math Practice Question

Let $$a \in \left( {0,{\pi \over 2}} \right)$$ be fixed. If the integral $$\int {{{\tan x + \tan \alpha } \over {\tan x - \tan \alpha }}} dx$$ = A(x) cos 2$$\alpha $$ + B(x) sin 2$$\alpha $$ + C, where C is a constant of integration, then the functions A(x) and B(x) are respectively :

1. A.$$x - \alpha $$ and $${\log _e}\left| {\cos \left( {x - \alpha } \right)} \right|$$
2. B.$$x + \alpha $$ and $${\log _e}\left| {\sin \left( {x - \alpha } \right)} \right|$$
3. C.$$x + \alpha $$ and $${\log _e}\left| {\sin \left( {x + \alpha } \right)} \right|$$
4. D.$$x - \alpha $$ and $${\log _e}\left| {\sin \left( {x - \alpha } \right)} \right|$$