Question

How do you find the value of `cos (tan^-1 (2/3))`?

Answer 1

`+-3/sqrt13`

Explanation:

Let `a =tan^(-1)(2/3)`.
As tan a = 2/3, cos a and sin a should both have the same sign and `a = tan^(-1)(2/3)=33.7^o or 213.7^o`, in `[0, 2pi]`.

So, I take a as either, and so, `cos a = cos(tan^(-1)(2/3))=+-3/sqrt13`.