The solution set of the equation 4sin⁡θcos⁡θ−2cos⁡θ−23sin⁡θ+3=0 in the interval (0,2π), is

The solution set of the equation 4sinθcosθ2cosθ23sinθ+3=0 in the interval (0,2π), is

  1. A

    3π4,7π4

  2. B

    π3,5π3

  3. C

    3π4,7π4,π3,5π3

  4. D

    π6,5π6,11π6

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    Solution:

    We have

    4sinθcosθ2cosθ23sinθ+3=02sinθ(2cosθ3)1(2cosθ3)=0(2cosθ3)(2sinθ1)=0cosθ=32 or, sinθ=12θ=π6,5π6,11π6

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