To simplify the given expression, we will use the trigonometric identity:

cos^2(x) - sin^2(x) = cos(2x)

Therefore, the given expression becomes:

cos(3x/2 - pi/6) > 1/2

Since we want to find when this expression is greater than 1/2, we will look at the possible values of cos(3x/2 - pi/6) that satisfy this inequality.

For cosine function, the values between 0 and pi/2 make the function positive. Therefore, the given expression is greater than 1/2 in this range.

Hence, the solution to the inequality is:

0 < 3x/2 - pi/6 < pi/2

Now, we need to solve for x:

0 < 3x/2 - pi/6 < pi/2
pi/6 < 3x/2 < 2pi/3
pi/3 < x < 4pi/9

Therefore, the solution to the inequality cos^2(3x/2-pi/6)-sin^2(3x/2-pi/6)>1/2 is x such that pi/3 < x < 4pi/9.