Since cos(X) = 1/sec(X): cos(X) = 8/9.
Knowing that cos = x/r ---> x = 8 and r = 9
Since x2 + y2 = r2 ---> 82 + y2 = 92 ---> 64 + y2 = 81 ---> y2 = 17
Since the angle is in the fourth quadrant, y is negative: y = - sqrt(17)
tan(X) = y/x = - sqrt(17) / 8