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Find the solutions to the equation on the interval $[0,2\pi ]$.

$$2+\cos { 2x=3\cos { x } } $$

A

$x=0,\cfrac { \pi }{ 3 } ,\cfrac { 5\pi }{ 3 } ,2\pi \quad $

B

$x=0,\cfrac { \pi }{ 3 }$

C

$x=\cfrac { 5\pi }{ 3 } ,2\pi \quad$

D

$x=\cfrac { \pi }{ 6 } ,\cfrac { \pi }{ 2 } ,\cfrac { 5\pi }{ 6 } $

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