Given: cos2x=(-5/12) and x is less than pi but greater than (pi/2)

Since this is your homework and not ours. What do you think the answer was and how did you arrive at it.

Hint: if you replace 2x with another variable, say w, then you have:

\cos w = - \frac 5 {12}, and \pi \le w \le 2 \pi.

Now, can you solve for w?