The solution set of the equation (2cosx−1)(3+2cosx)=0 in 0≤x≤2π is

(2cosx−1)(3+2cosx)=0 cosx=12 or cosx=−32 Case-1: cosx=12 x=π3,5π3 Case-2: cosx=−32 is not possible. (∵−1≤cosx≤1 )

(2cosx−1)(3+2cosx)=0 cosx=12 or cosx=−32 Case-1: cosx=12 x=π3,5π3 Case-2: cosx=−32 is not possible. (∵−1≤cosx≤1 )

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The solution set of the equation $(2 \cos x - 1) (3 + 2 \cos x) = 0$ in $0 \leq x \leq 2 π$ is

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{\frac{π}{3}, \frac{5 π}{3}}

{\frac{π}{2}, \frac{3 π}{2}}

{\frac{π}{3}, \frac{π}{2}}

{\frac{π}{2}, π}

answer is B.

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(2 \cos x - 1) (3 + 2 \cos x) = 0

$\cos x = \frac{1}{2}$ or $\cos x = - \frac{3}{2}$

Case-1:

$\cos x = \frac{1}{2}$

$x = \frac{π}{3}, \frac{5 π}{3}$

Case-2:

$\cos x = - \frac{3}{2}$ is not possible. $(∵ - 1 \leq \cos x \leq 1)$

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