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 :

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 :

$x - \alpha $ and ${\log _e}\left| {\cos \left( {x - \alpha } \right)} \right|$

$x + \alpha $ and ${\log _e}\left| {\sin \left( {x - \alpha } \right)} \right|$

$x + \alpha $ and ${\log _e}\left| {\sin \left( {x + \alpha } \right)} \right|$

$x - \alpha $ and ${\log _e}\left| {\sin \left( {x - \alpha } \right)} \right|$

Solution

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