Search any question & find its solution
Question:
Answered & Verified by Expert
If $\int \frac{\sin x}{\sin (x-\alpha)} d x=A x+B \log \sin (x-\alpha)+C$, then value of $(A, B)$ is
Options:
Solution:
1966 Upvotes
Verified Answer
The correct answer is:
$(\cos \alpha, \sin \alpha)$
$(\cos \alpha, \sin \alpha)$
Put $x-\alpha=t$
$\Rightarrow \int \frac{\sin (\alpha+t)}{\sin t} d t=\sin \alpha \int \cot t d t+\cos \alpha \int d t$
$=\cos \alpha(x-\alpha)+\sin \alpha \ln |\sin t|+c$
$A=\cos \alpha, B=\sin \alpha$
$\Rightarrow \int \frac{\sin (\alpha+t)}{\sin t} d t=\sin \alpha \int \cot t d t+\cos \alpha \int d t$
$=\cos \alpha(x-\alpha)+\sin \alpha \ln |\sin t|+c$
$A=\cos \alpha, B=\sin \alpha$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.