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Let a ∈ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π 2 , 0 be fixed. If the integral ∫ α α + tan – x tan tan x tan dx = A(x) cos 2 α + B(x) sin 2 α + C, where C is a constant of integration, then the functions A(x) and B(x) are respectively :

1. x – α and log e |cos(x – α )|
2. x + α and log e |sin(x – α )|
3. x + α and log e |sin(x + α )|
4. x – α and log e |sin(x – α )|

Correct answer: x – α and log e |sin(x – α )|

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