Question

The solution set of $(2\cos x-1)(3+2\cos x)=0$ in the interval $0\le x\le 2\pi$ is-

• A. $\left(\pi \right)/3,\left(5\pi \right)/3$
• B. $\left(\pi \right)/3,\left(\pi \right)/2$
• C. $\pi /3,{\cos }^{-1}(-3/2)$
• D. $Noneofthese$

Answer 1

The correct option is A $\left(\pi \right)/3,\left(5\pi \right)/3$

Given

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

$⟹(2\cos x-1)=0$

$⟹\cos x=\frac{1}{2}$

$\cos x=\cos \frac{\pi }{3}$

$x=2n\pi \pm \frac{\pi }{3}$

$x=\frac{\pi }{3},\frac{5\pi }{3}$