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/pi/6 < 3x/2 < 2pi/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.
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/
pi/6 < 3x/2 < 2pi/
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.