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Q.

The solution set of the equation 4sinθ.cosθ−2cosθ−23sinθ+3=0 in the interval (0,2π) is

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a

{3π4,7π4}

b

{π3,5π3}

c

{3π4,π,π3,5π3}

d

{π6,5π6,11π6}

answer is D.

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Detailed Solution

4sinθ.cosθ−2cosθ−23sinθ+3=0 ⇒2cosθ(2sinθ−1)−3(2sinθ−1)=0 ⇒(2sinθ−1)(2cosθ−3)=0 ⇒sinθ=12,32⇒θ=π6,5π6,11π6

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The solution set of the equation 4sinθ.cosθ−2cosθ−23sinθ+3=0 in the interval (0,2π) is