Answer
$\frac{\sqrt 5}{5}$
Work Step by Step
Recall: $\cos(\arctan x)=\frac{1}{\sqrt {1+x^{2}}}$
$\implies\cos(\arctan (2))=\frac{1}{\sqrt {1+2^{2}}}=\frac{1}{\sqrt {5}}=\frac{\sqrt 5}{5}$
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