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Given the following two equations, find the exact solutions that they have in common in the interval $[0,2\pi )$.

a. $\sin { 2x+\cos { x=0 } } $
b. $\sin { 2x\sin { x=\cos { x } } } $

A

$ x=\cfrac { \pi }{ 4 } ,\cfrac { 3\pi }{ 4 } ,\cfrac { 5\pi }{ 4 } ,\cfrac { 7\pi }{ 4 }$

B

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

C

$ x=\cfrac { \pi }{ 2 } ,\cfrac { 3\pi }{ 2 } ,\cfrac { \pi }{ 4 } ,\cfrac { 3\pi }{ 4 } ,\cfrac { 5\pi }{ 4 } ,\cfrac { 7\pi }{ 4 }$

D

None of the exact solutions are same

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