Use the half-angle formula to find the exact value of cos(x/2) when tanx = -5/8 and x is in quadrant IV. (| is a radical)

Question

==> I got sqrt((89 + 8sqrt(89))/178). Is this correct? I hope my answer is easy to read..

Answer 1

The answer is correct.
In fact, you have nicely rationalized the denominator, which is expected of students.
You could also express the answer as:
cos(x)=sqrt((1/2)+4sqrt(89)/89)
if it appeals to you.