Let `alpha in (0, pi//2)` be fixed. If the integral `int("tan x" + "tan" alpha)/("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.

Options

A. `x +alpha` and `log_(e)|sin (x+alpha)|`
B. `x - alpha` and `log_(e)|sin (x-alpha)|`
C. `x - alpha` and `log_(e) |cos (x-alpha)|`
D. `x +alpha` and `log_(e)|sin (x-alpha)|`

Answer

A