Find:
\int \frac{\sin \left ( x-a \right )}{\sin \left ( x+a \right )}dx

 

 

 

 
 
 
 
 

Answers (1)

Let I= \int \frac{\sin \left ( x-a \right )}{\sin \left ( x+a \right )}dx
\Rightarrow I= \int \frac{\sin \left [ \left ( x+a \right )-2a \right ]}{\sin \left ( x+a \right )}dx
\Rightarrow I= \int \frac{\sin \left ( x+a \right )\cos \left ( 2a \right )-\cos \left ( x+a \right )\sin \left ( 2a \right )}{\sin \left ( x+a \right )}dx
\Rightarrow \int \cos \left ( 2a \right )dx-\int \cot \left ( x+a \right )\cdot \sin \left ( 2a \right )dx
\Rightarrow x\cos 2a-\log \left | \sin \left ( x+a \right ) \right |\cdot \sin 2a+C

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