To solve for x in the equation sin^2(2x) - cos^2(2x) = 1/2, we can use the trigonometric identity sin^2(x) - cos^2(x) = -cos(2x).
Therefore, the equation simplifies to -cos(2x) = 1/2.
We can then find the value of cos(2x) by rearranging the equation:
cos(2x) = -1/2
Now, we need to find the values of x that satisfy this equation. Since the cosine function alternates between -1 and 1, we need to find the angles where cos(2x) = -1/2.
One such angle is 2x = 2π/3 + 2πn, where n is an integer. Dividing by 2, we get x = π/3 + πn.
Therefore, the solution to the equation sin^2(2x) - cos^2(2x) = 1/2 is x = π/3 + πn, where n is an integer.
To solve for x in the equation sin^2(2x) - cos^2(2x) = 1/2, we can use the trigonometric identity sin^2(x) - cos^2(x) = -cos(2x).
Therefore, the equation simplifies to -cos(2x) = 1/2.
We can then find the value of cos(2x) by rearranging the equation:
cos(2x) = -1/2
Now, we need to find the values of x that satisfy this equation. Since the cosine function alternates between -1 and 1, we need to find the angles where cos(2x) = -1/2.
One such angle is 2x = 2π/3 + 2πn, where n is an integer. Dividing by 2, we get x = π/3 + πn.
Therefore, the solution to the equation sin^2(2x) - cos^2(2x) = 1/2 is x = π/3 + πn, where n is an integer.