Question

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

Answer 1

`1/sqrt5`

Explanation:

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`