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## QuestionMathsClass 11

The solution set of the equation $$4\sin\theta \cos\theta -2\cos\theta -2\sqrt{3}\sin\theta +\sqrt{3}=0$$ in the interval $$(0, 2\pi )$$ is（ ）
A. $$\left\{\frac{3\pi }{4},\frac{7\pi }{4}\right\}$$
B. $$\left\{\frac{\pi }{3},\frac{5\pi }{3}\right\}$$
C. $$\left\{\frac{3\pi }{4},\pi ,\frac{\pi }{3},\frac{5\pi }{3}\right\}$$
D. $$\left\{\frac{\pi }{6},\frac{5\pi }{6},\frac{11\pi }{6}\right\}$$

D
4.6
4.6

## Solution

$$4\sin\theta \cos\theta -2\cos\theta -2\sqrt{3}\sin\theta +\sqrt{3}=0$$
$$\Rightarrow 2 \cos\theta(2\sin\theta-1) -\sqrt3{(2\sin\theta-1)}=0$$
$$\Rightarrow (2\cos\theta-\sqrt3){(2\sin\theta-1)}=0$$
$$\Rightarrow \cos\theta=\dfrac{\sqrt3}{2}$$ and $$\sin\theta =\dfrac{1}{2}$$
In interval $$(0,2\pi)$$,
$$\theta =\dfrac{\pi}{6}, \dfrac{5\pi}{6}$$ and $$\dfrac{11\pi}{6}$$
Hence, option D is correct.