Use the Cofunction Identities to Find an Angle That Makes $\tan \frac { x } { 2 }$

Multiple Choice

Use the cofunction identities to find an angle that makes the statement true.
-Find $\tan \frac { x } { 2 }$ , given that $\tan x = 3$ and $x$ terminates in $\pi < x < \frac { 3 \pi } { 2 }$ .

A) $\frac { \sqrt { 10 } + 1 } { - 3 }$
B) $\frac { \sqrt { 10 } - 1 } { - 3 }$
C) $\frac { \sqrt { 10 } - 1 } { 3 }$
D) $\frac { \sqrt { 10 } + 1 } { 3 }$