How do you find the exact value for $cos(arctan(2))$ ?

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Answer 1 · 2015-06-23T17:55:04

$1/sqrt5$

Let arc tan 2=u, so that tan u =2
Now square both sides, $tan^2 u= 4$
Add 1 on both sides, $sec^2 u= 5$
$cos^2 u= 1/5$

cos u= $1/sqrt5$ , u=arc $cos( 1/sqrt5)$ = arc tan 2

cos arc tan2= cos arc $cos (1/sqrt5)$ = $1/sqrt5$

How do you find the exact value for cos(arctan(2)) cos(arctan(2)) ?