The given equation is 2cos²(4x) - 1 = 0. To determine if 16 is a solution for this equation, we need to substitute 16 in place of x and solve for the equation.
1. Substitute x = 16 into the equation:
2cos²(4(16)) - 1 = 0
2cos²(64) - 1 = 0
2. Simplify the expression:
2cos²(64) = 1
cos²(64) = 1/2
3. Since the range of cosine function is [-1, 1], and cos²(64) = 1/2 which is within the range, it means that 16 is a valid solution for the given equation.
Therefore, the statement "16 is a solution for the equation 2cos²(4x) - 1 = 0" is True.
