Cos5x+cos3x=3cos4x X принадлежит {0;pi} Helllllopppppppp

Question

Cos5x+cos3x=3cos4x
X принадлежит {0;pi}
Helllllopppppppp

Answer 1

2Cos4x Cos x = 3Cos 4x
2Cos4x Cosx - 3Cos4x = 0
Cos4x(2Cosx - 3) = 0
Cos4x = 0              или               2Cosx -3 = 0
4x = π/2 + πn , n ∈Z                    Cosx = 3/2(нет решений)
x = π/8 + πn/4, n ∈Z