Final answer:
The equation 2 cos² (4x) -1=0 can be solved by finding the values of x in degrees that satisfy the equation.
Step-by-step explanation:
The equation 2 cos² (4x) -1=0 can be rewritten as cos² (4x) = 1/2. Solving for cos (4x), you take the square root of both sides to get cos (4x) = ± sqrt(1/2). Since the cosine function repeats itself every 360 degrees, you can find one solution in the first quadrant and another solution in the second quadrant. To find the value of x, you divide 4x by 4 and then divide the corresponding angles by 4. So the solutions are x = 45 degrees/8 or x = 135 degrees/8.
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