∫1sin⁡(x−a)sin⁡(x−b)dx=

1sin(xa)sin(xb)dx=

  1. A

    1sin(ab)logsin(xa)sin(xb)+C

  2. B

    1sin(ab)logsin(xa)sin(xb)+C

  3. C

    logsin(xa)sin(xb)+C

  4. D

    logsin(xa)sin(xb)+C

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    Solution:

    We have, 

    1sin(xa)sin(xb)dx=1sin(ba)sin{(xa)(xb)}sin(xa)sin(xb)dx=1sin(ba){cot(xb)cot(xa)}dx=1sin(ba){logsin(xb)logsin(xa)}+C=1sin(ba)logsin(xb)sin(xa)+C=1sin(ab)logsin(xa)sin(xb)+C

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