Find the Exact Value by Using a Half-Angle Identity $\cos x$

Multiple Choice

Find the exact value by using a half-angle identity.
-Write $\cos x$ in terms of $\cot x$ .

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