sin(x) - cos(2x) = 0sin(x) - (1 - 2sin^2(x)) = 0sin(x) - 1 + 2sin^2(x) = 02sin^2(x) + sin(x) - 1 = 0
Решаем уравнение квадратного вида:D = 1 + 8 = 9
sin(x) = (-1 ± √9) / 4
sin(x) = (-1 ± 3) / 4
sin(x) = -1/4x = arcsin(-1/4) + 2πn, x = π - π/4 + 2πn, x = 3π/4 + 2πn
sin(x) = 1x = arcsin(1) + 2πn, x = π/2 + 2πn
Ответ: x = 3π/4 + 2πn, x = π/2 + 2πn, где n - любое целое число.
sin(x) - cos(2x) = 0
sin(x) - (1 - 2sin^2(x)) = 0
sin(x) - 1 + 2sin^2(x) = 0
2sin^2(x) + sin(x) - 1 = 0
Решаем уравнение квадратного вида:
D = 1 + 8 = 9
sin(x) = (-1 ± √9) / 4
sin(x) = (-1 ± 3) / 4
sin(x) = -1/4
x = arcsin(-1/4) + 2πn, x = π - π/4 + 2πn, x = 3π/4 + 2πn
sin(x) = 1
x = arcsin(1) + 2πn, x = π/2 + 2πn
Ответ: x = 3π/4 + 2πn, x = π/2 + 2πn, где n - любое целое число.