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integrate sin(x-a)dx/sin(x+a)

integrate sin(x-a)dx/sin(x+a)

Grade:12

2 Answers

vikas askiitian expert
509 Points
10 years ago

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

Rishi Sharma
askIITians Faculty 646 Points
9 months ago
Dear Student,
Please find below the solution to your problem.

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

Thanks and Regards

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