The most general solution of21+|cos⁡x|+cos2⁡x+cos3⁡x+…=4  is given by

The most general solution of

21+|cosx|+cos2x+cos3x+=4  is given by

  1. A

    x=nπ±π3,nZ

  2. B

    z=2nπ±π3nZ

  3. C

    x=2nπ±2π3,nZ

  4. D

    none of these

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    Solution:

    The given equation is not meaningful for 

    |cosx|=1. So, let |cosx|1.

    Now,

       21+|cosx|+cos2x+|cosx|3++tosx=4

     121|cosx|=22 11|cosx|=2 22|cosx|=1 |cosx|=12 cosx=±12 cosx=cosπ3,cosx=cos2π3 x=2nπ±π3,x=2nπ±2π3,nZ x=2nπ±π3,x=(2n±1)π±π3 x=nπ±π3,nZ.

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