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

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Answer 1 · 2016-05-27T04:31:16

$-3/5$ .

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 $cos 2a = 2 cos^2 a - 1 = 2/5-1=-3/5$

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