Question

If tanx= -1/3, cos>0, then how do you find cos2x?

Answer 1

`cos 2x = 4/5`

Explanation:

`tan x = -1/3`, and cos x > 0. First, find cos x
Use trig identity:
`cos ^2 x = 1/(1 + tan^2 x) = 1/(1 + 1/9) = 9/10`
`cos x = 3/sqrt10 = (3sqrt10)/10` (cos x > 0)
Next, use trig identity:
`cos 2x = 2cos^2 x - 1`
In this case:
`cos 2x = 2(9/10) - 1 = 9/5 - 5/5 = 4/5`

Answer 2

`cos 2x = 4/5 = 0.8`

Explanation:

Identity : `cos 2x = (1 - tan^2 x) / (1 + tan^2 x)`

Given : `tan x = -1/3`

`:. cos 2x = (1 - (-1/3)^2) / (1 + (-1/3)^2)`

`cos 2x = (1 - 1/9) / (1 + 1/9)`

`cos 2x = (8/9) / (10/9) = 8/10 = 4/5 = 0.8`