Question

How do you evaluate `cos(2 arctan (-2))`?

Answer 1

`-3/5`.

Explanation:

Let `a = arc tan (-2)`. Then, `tan a = -2 < 0`. a is in the 2nd quadrant

or in the 4th. So, `cos a = +-1/sqrt 5`

The given expression is `cos 2a = 2 cos^2 a - 1 = 2/5-1=-3/5`