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Considering only the principal values, if $\tan ({\cos ^{ - 1}}x)$ $ = \sin \left[ {{{\cot }^{ - 1}}\left( {\frac{1}{2}} \right)} \right]$, then $x$ is equal to

• A
  $\frac{1}{{\sqrt 5 }}$
• B
  $\frac{2}{{\sqrt 5 }}$
• C
  $\frac{3}{{\sqrt 5 }}$
• ✓
  $\frac{{\sqrt 5 }}{3}$