Question

Evaluate cos(2Arctan(3/4) )

I know the answer is 7/25 but i'm not sure how to get the answer

Answer 1

this can be confusing

but we we start with
tan A = 3/4
and take the arc tangent of both sides (this "undoes" the tangent), we get
A = arctan(3/4)

so we see that A = arctan(3/4) corresponds to tan A = 3/4

next, we see we want to find
cos (2 * arctan(3/4) )
using A = arctan(3/4), this is asking for

cos (2A)

Answer 2

How do we find the cosine of 2A ?
This will take multiple steps

We start with
A = arctan(3/4) and as noted above, this means
tan A = 3/4

draw a triangle: