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JEE Main 2019 · 12 April · Shift II

JEE Main 2019 Mathematics question on Indefinite Integration

Let α∈(0,π/2)\alpha \in (0, \pi/2) be fixed. If the integral ∫tan⁡x+tan⁡αtan⁡x−tan⁡αdx=A(x)cos⁡2α+B(x)sin⁡2α+C\int \frac{\tan x + \tan \alpha}{\tan x - \tan \alpha} dx = A(x) \cos 2\alpha + B(x) \sin 2\alpha + C, where CC is a constant of integration, then the functions A(x)A(x) and B(x)B(x) are respectively
  1. A.
    x+αx + \alpha and log⁡e∣sin⁡(x+α)∣\log_e |\sin(x + \alpha)|
  2. B.
    x−αx - \alpha and log⁡e∣sin⁡(x−α)∣\log_e |\sin(x - \alpha)|
  3. C.
    x−αx - \alpha and log⁡e∣cos⁡(x−α)∣\log_e |\cos(x - \alpha)|
  4. D.
    x+αx + \alpha and log⁡e∣sin⁡(x−α)∣\log_e |\sin(x - \alpha)|
Show answer

Correct option: B

[JEE Main 2019 · 12 April · Shift II]

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