What is the length of the longest interval in which the function f(x) = 2cos²x - 1 is decreasing?

f(x) = 2cos²x - 1 = cos(2x). f'(x) = -2sin(2x). For decreasing, f'(x) < 0, i.e., sin(2x) > 0, which holds when 2x ∈ (0, π), i.e., x ∈ (0, π/2). The longest such interval has length π/2.