|Nasser M. Abbasi|
It looks like you are correct, looks like a bug. I send email to firstname.lastname@example.org just in case. I get the wrong answer also on version 9.
I verified on 2 other CAS systems also, and they both return the -1/2 (1/sin(x)^2) answer, not the Mathematica answer (which has an extra cos(x)^2 in the numerator)