Question

How do you evaluate `cos(2cos^-1(1/7))`?

Answer 1

`-47/49`, about `-0.9592`. See below.

Explanation:

Let `\theta=\arccos(1/7)`. Thus `\cos\theta=1/7`. From the double-angle formula for cosine:

`\cos(2\arccos(1/7))`
`=\cos(2\theta)`
`=2\cos^2\theta-1`
`=2(1/7)^2-1=-47/49`