The general solution of the trigonometrical equation sin⁡x+cos⁡x=1 for n=0,±1,… is given by

The general solution of the trigonometrical equation sinx+cosx=1 for n=0,±1, is given by

  1. A

    x=2nπ

  2. B

    x=2nπ+π2

  3. C

    x=nπ+(1)nπ4π4

  4. D

    none of these

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    Solution:

    We have

    sinx+cosx=12sinxcosπ4+cosxsinπ4=1sinx+π4=12sinx+π4=sinπ4x+π4=nπ+(1)nπ4,nZ

     x=nπ+(1)nπ4π4,nZ

     

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