Posted by terra on Friday, September 2, 2011 at 9:31pm.
Simplify by referring to the appropriate triangle or trigonometric identity:
cos(arctan(x))

math  Reiny, Friday, September 2, 2011 at 9:50pm
sketch a rightangled triangle with some angle Ø
, label the opposite side x and the adjacent side 1
(this way tanØ = x/1 , and Ø = arctan(x/1)
the hypotenuse would be √(x^2 + 1)
and
cosØ = 1/√(x^2+1)