If cos⁡3x+sin⁡2x−7π6=−2 then x=

If cos3x+sin2x7π6=2 then x=

  1. A

    π3(6k+1),kZ

  2. B

    π3(6k1),kZ

  3. C

    π3(2k+1),kZ

  4. D

    none of these

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    Solution:

    We have

    cos3x+sin2x7π6=21+cos3x+1+sin2x7π6=0(1+cos3x)+1cos2x2π3=02cos23x2+2sin2xπ3=0cos3x2=0 and sinxπ3=03x2=π2,3π2, and xπ3=0,π,2πx=π3

    Therefore, the general solution is given by

    x=2kπ+π3=π3(6k+1), where kZ.

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