1) 2sin(x/2) = 1 - cosx
cosx = cos(2*x/2) = 1 - 2sin^2(x/2) - по формуле двойного угла
2sin(x/2) = 1 - 1 + 2sin^2(x/2)
2sin^2(x/2) - 2sin(x/2) = 0
2sin(x/2) * (sin(x/2) - 1) = 0
sin(x/2) = 0, x/2 = πk, x = 2πk
sin(x/2) = 1, x/2 = π/2 + 2πk, x = π + 4πk
2) cos(3π/2 + x)*cos(3x) - cos(π - x)*sin(3x) = -1
cos(3π/2 + x) = cos(2π - π/2 + x) = cos(π/2 - x) = sinx - формула приведения
cos(π - x) = -cosx - формула приведения
sinx*cos(3x) + cosx*sin(3x) = -1 - слева формула суммы аргументов синуса
sin(3x + x) = -1
sin(4x) = -1
4x = -π/2 + 2πk
x = -π/8 + πk/2
(или 4x = 3π/2 + 2πk, x=3π/8 + πk/2)