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

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a
3π4,7π4
b
π3,5π3
c
3π4,7π4,π3,5π3
d
π6,5π6,11π6

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detailed solution

Correct option is D

We have

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

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