Use the properties of inverse functions to evaluate the expression.?

Question

cos(arctan1)

Answer 1

Let t = arctan(1). Then
tan(t) = 1

tan is equal to 1 at the point pi/4. Therefore,

cos(arctan(1)) = cos(pi/4) = sqrt(2)/2

Answer 2

arctan 1 = (a) (360n) + 45 degrees or (b) (360n) + 235 degrees, for all integer values a ' n.'.

Therefore cos(arctan1) = (a) 1/2^(1/2) or (b) = - 1/2^(1/2).

Live long and prosper.

Answer 3

cos(arctan1) = cos(π/4) = 1/√2