Write the Following Expression as an Algebraic Expression That Does $\sin ^ { 2 } \left( \tan ^ { - 1 } 2 x \right)$

Multiple Choice

Write the following expression as an algebraic expression that does not involve trigonometric or inverse trigonometric functions $\sin ^ { 2 } \left( \tan ^ { - 1 } 2 x \right)$

A) $\frac { x ^ { 2 } } { 1 + 2 x ^ { 2 } }$
B) $\frac { 2 x ^ { 2 } } { 1 + 2 x ^ { 2 } }$
C) $\frac { 2 x ^ { 2 } } { 1 + 4 x ^ { 2 } }$
D) $\frac { 4 x ^ { 2 } } { 1 + 4 x ^ { 2 } }$