Find the Exact Value of the Expression, If Possible $\cos \left( \tan ^ { - 1 } x \right)$

Multiple Choice

Find the exact value of the expression, if possible. Do not use a calculator.
- $\cos \left( \tan ^ { - 1 } x \right)$

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