How do you evaluate $cos(Arctan 2)$ ?

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Answer 1 · 2016-06-10T17:44:35

Set $x=arctan2$ hence $tanx=2$ square both sides to get

$tan^2x=4=>tan^2x+1=5=>1/cos^2x=5$

Hence $cosx=1/sqrt5$ or $x=arccos(1/sqrt5)$

But $x=arctan2$ hence

$arctan2=arccos(1/sqrt5)=>cos(arctan2)=cos(arccos(1/sqrt5))=1/sqrt5$

Finally $cos(arctan2)=1/sqrt5$

How do you evaluate cos(Arctan 2)cos(Arctan 2)?