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Let alpha in (0, pi//2) be fixed. If the...

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.

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+alpha )|`

D

`(x + alpha ) and log_e | cos (x-alpha)|`

Text Solution

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The correct Answer is:
B
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