1) 2sin(4Π/3-x) - sin(4Π/3+x) = 0
По формулам синуса суммы
2*(sin(4Π/3)*cos x-cos(4Π/3)*sin x) - (sin(4Π/3)*cos x+cos(4Π/3)*sin x) = 0
2*(-√3/2)*cos x-2*(-1/2)*sin x - (-√3/2)*cos x - (-1/2)*sin x = 0
-√3*cos x + sin x + √3/2*cos x + 1/2*sin x = 0
-√3/2*cos x + 3/2*sin x = 0
Делим всё на √3 и умножаем на 2.
-cos x + √3*sin x = 0
√3*sin x = cos x
Делим все на cos x и на √3
tg x = 1/√3
x = Π/6 + Π*k
2) sin x*sin 3x + cos 4x = 0
sin x*sin 3x + cos(x+3x) = 0
sin x*sin 3x + cos x*cos 3x - sin x*sin 3x = 0
cos x*cos 3x = 0
cos x = 0; x = Π/2+Π*k
cos 3x = 0; x = Π/6+Π/3*n