Let \\alpha \in(0, \\pi / 2) be fixed. If the integral \int\frac{\tan x+\tan \\alpha}{\tan x-\tan \\alpha} d x=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 [12 Apr 2019 Shift 2]

Correct Answer is : x−α and loge|sin(x−α)|

x-\\alpha and \log _{e}|\cos (x-\\alpha)|

x-\\alpha and \log _{e}|\sin (x-\\alpha)|

x+\\alpha and \log _{e}|\sin (x+\\alpha)|

x+\\alpha and \log _{e}|\sin (x-\\alpha)|

Indefinite Integrals

Section: Mathematics

Question : 55 of 89

Marks: +1, -0

Let α∈(0,

) be fixed. If the integral

∫

tan‌x+tan‌α

tan‌x−tan‌α

dx=A(x)‌cos‌2‌α+B(x)‌sin‌2‌α+C

where c is a constant of integration, then the functions A(x) and B(x) are respectively

[12 Apr 2019 Shift 2]

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