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)|sin(x-alphas)|`
D. `x+alpha` and `log_(e)|sin(x-alpha)|`

Answer

A

Explanation

`int(sin(x+alpha))/(sin(x-alpha))dx`
`x-alpha=timpliesx=t+alpha`
`int(sin(t+2alpha))/(sin t) dt`
`cos(2 alpha)t+sin 2 alpha In |sin t|+c`