Let a (0,(π)/2) be fixed. If the integral ∫ (tan x + tan α)/(tan x - tan α) 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:

(D) x - α and log e | sin (x - α) |

(A) x - α and log e | cos (x - α) |

(B) x + α and log e | sin (x - α) |

(C) x + α and log e | sin (x + α) |

Integral Calculus: JEE Main 2019 Mathematics question

JEE Main 2019 · 12 Apr, Evening shift · Q4010

JEE Main 201912 Apr, Evening shiftMathematicsHardIntegral Calculus369× since 2002

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 :

JEE Main 2019 Integral Calculus Question with Solution (12 Apr Evening shift, Q4010) | JEE Arc