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Integrate the function Sin(x-a)/sinx+a) with respect to x

Integrate the function
Sin(x-a)/sinx+a) with respect to x

Grade:12

1 Answers

Arun
25763 Points
3 years ago
Dear Devesh
 
 

I={sinx-a/sinx+a }dx

 

put x+a=t

 

  so    dx=dt

 

 I={sin(t-2a) /sint }dt                     (sina-b=sinacosb-cosasinb)

 

 I ={sintcos2a -costsin2a/sint }dt

 

 I ={cos2a - cottsin2a}dt

 

 I={tcos2a -sin2alogsint} +c

 

 I={(x+a)cos2a-sin2a.logsin(x+a)} + c

 

 

Regards

Arun (askIITians forum expert)

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