Question

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

Answer 1

Substitute the value of `x` for `x`; evaluate `tan^(-1)(x)`; multiply by 2; evaluate the `cos` of the result.

Explanation:

Perhaps you meant:
"Find the value of `x` for which `cos(2tan^(-1)(x))=0`"
or something similar (???)

otherwise we have a question like:
"Find the value of `x+2`"