Let a ∈ (0,π/2) be fixed. If the integral ∫ tan x + tan α/tan x - tan α dx = A(x) cos 2α + B(x) sin 2α + C, where C is a constant of integration, then the functions A(x) and B(x) are respectively :

(1) x – α and loge|cos(x – α)|
(2) x + α and loge|sin(x – α)|
(3) x + α and loge|sin(x + α)|
(4) x – α and loge|sin(x – α)|