The number of solutions of the equation sin5⁡x−cos5⁡x=1cos⁡x−1sin⁡x(sin⁡x≠cos⁡x) is 

 The number of solutions of the equation sin5xcos5x=1cosx1sinx(sinxcosx) is 

  1. A

    0

  2. B

    1

  3. C

    infinite

  4. D

    None of these

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    Solution:

    sin5xcos5x=sinxcosxsinxcosxsinxcosxsin5xcos5xsinxcosx=1 12sin2xsin4x+sin3xcosx+sin2xcos2x+sinxcos2x+cos4x=1 sin2xsin2x+cos2x22sin2xcos2x+sinxcosxsin2x+cos2x+sin2xcos2x=2 sin2x1sin2xcos2x+sinxcosx=2 sin32x2sin22x4sin2x+8=0 (sin2x2)2(sin2x+2)=0

    sin2x=±2, which is not possible for any x

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