The following question appeared in an examination:
Given that $\tan x = \sqrt { 3 }$, find the possible values of $\sin 2 x$.
A student gave the following answer:
$$\begin{aligned} & \tan x = \sqrt { 3 } \text { so } x = 60 ^ { \circ } \text { and } 2 x = 120 ^ { \circ } \\ & \text { therefore } \sin 2 x = \frac { \sqrt { 3 } } { 2 } \end{aligned}$$
Which one of the following statements is correct?
A $\frac { \sqrt { 3 } } { 2 }$ is the only possible value, and this is fully supported by the reasoning given in the student's answer.
B $\frac { \sqrt { 3 } } { 2 }$ is the only possible value, but the reasoning given should consider other possible values of $x$ for which $\tan x = \sqrt { 3 }$.
C $\frac { \sqrt { 3 } } { 2 }$ is the only possible value, but the reasoning given should consider other possible values of $x$ for which $\sin 2 x = \frac { \sqrt { 3 } } { 2 }$.
D $\frac { \sqrt { 3 } } { 2 }$ is not the only possible value because the reasoning given should have considered other possible values of $x$ for which $\tan x = \sqrt { 3 }$.
E $\frac { \sqrt { 3 } } { 2 }$ is not the only possible value because the reasoning given should have considered other possible values of $x$ for which $\sin 2 x = \frac { \sqrt { 3 } } { 2 }$.