If ∫sin⁡xsin⁡(x−α)dx=Ax+Blog⁡sin⁡(x−α)+C, , then the value of (A, B), is

If sinxsin(xα)dx

=Ax+Blogsin(xα)+C, , then the value of (A, B), is

  1. A

    (cosα,sinα)

  2. B

    (cosα,sinα)

  3. C

    (sinα,cosα)

  4. D

    (sinα,cosα)

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    Solution:

    We have,

    sinxsin(xα)dx=sin(xα+α)sin(xα)dx=sin(xα)cosα+cos(xα)sinαsin(xα)dx=cosαdx+sinαcot(xα)dx=xcosα+sinαlog|sin(xα)|+CA=cosα,B=sinα (A,B)=(cosα,sinα)

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