is the same as
a square is NEVER negative. Therefore, if it is possible for cos(x) to equal zero, then zero must be your minimum.
cos(x) does have a positive maximum and a "negative maximum" (normally called a minimum).
Find the one that has the highest absolute value (in this case, it does not matter, since they both have the same absolute value).
Now, square that value, and that will be the maximum of (cos(x))^2
Just remember that the square of -1 is +1.