cos(2x) - 1 = 2^(1/2)(sin(5π/2 - x)
sin(5π/2) = -1cos(5π/2) = 0
cos(2x) - 1 = -2^(1/2)cos(x)
2cos^2(x) - 1 - 1 = -2^(1/2)
2cos^2(x) = 2^(1/2)cos^2(x) = 2^(1/2) / 2cos^2(x) = √2 / 2cos(x) = ±√(√2 / 2) = ±(√2 / 2 * 1/2^(1/2)) = ±(√2 / 2^(3/2)) = ±(√2 / 2√2) = ±1/2
cos(x) = ±1/2
x = π/3, -π/3, 5π/3, -5π/3.
cos(2x) - 1 = 2^(1/2)(sin(5π/2 - x)
sin(5π/2) = -1
cos(5π/2) = 0
cos(2x) - 1 = -2^(1/2)cos(x)
2cos^2(x) - 1 - 1 = -2^(1/2)
2cos^2(x) = 2^(1/2)
cos^2(x) = 2^(1/2) / 2
cos^2(x) = √2 / 2
cos(x) = ±√(√2 / 2) = ±(√2 / 2 * 1/2^(1/2)) = ±(√2 / 2^(3/2)) = ±(√2 / 2√2) = ±1/2
cos(x) = ±1/2
x = π/3, -π/3, 5π/3, -5π/3.