Question

How do you simplify `cos[2(tan^(-1)(-4/3))]`?

Answer 1

`-7/25`

Explanation:

Let `a = tan^(-1)(-4/3) in Q4`.

Then, `tan a = -4/3 < -1 = tan -(pi/4)`. So, `2a < -pi/2 and in Q3`.

And so, cos a = 3/5 and cos 2a < 0. .

The given expression is

`cos 2a =2 cos^2a-1= 2(3/5)^2-1=-7/25`.