Mathematics

# If $\int { \cfrac { \sin { x } }{ \sin { \left( x-\alpha \right) } } } dx=Ax+B\log { \sin { \left( x-\alpha \right) } } +c$, then the value of $(A,B)$ is-

$\left( \cos { \alpha } ,\sin { \alpha } \right)$

##### SOLUTION
$\displaystyle \int \frac{sin(x-\alpha +\alpha )}{sin(x-\alpha )}dx$
$\displaystyle \int \frac{sin(x-\alpha )cos\alpha +cos(x-\alpha )sin\alpha }{sin(x-\alpha )}$
$\displaystyle \int (cos\alpha +sin\alpha \,cot(x-\alpha ))dx$
$xcos\alpha +sin\alpha ln sin(x-\alpha )+c$
$A = cos\alpha$
$B = sin\alpha$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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