Let α∈(0,π/2) be fixed. If the integral ∫tan x+tan α/tan x−tan α dx=A(x)cos2α+B(x)sin2α+C, where C is a constant of integration, then the functions A(x) and B(x) are respectively:
A. x−α and log e|sin(x−α)|
B. x+α and log e|sin(x−α)|
C. x−α and log e|cos(x−α)|
D. x+α and log e|sin(x+α)|