Question

cos5x+cos2x+cos3x+cos4x=0

Answer 1

(Cos 5x + Cos 2x) + ( Cos3x + Cos 4x) = 0
2Cos3,5xCos1,5x + 2Cos3,5xCos0,5x=0
2 Cos3,5x(Cos1,5x+Cos0,5x) = 0
2Cos 3,5x·2CosxCos0,5x = 0
Cos 3,5x = 0           или     Cos x = 0         или     Cos0,5x = 0
3,5х = π/2 + πк, к ∈Z;   х = π/2 + πn, n ∈Z;  0,5x = π/2 + πm,m∈Z
х =π/7 +7πк/2,к∈Z                                          x =π + 2πm,m∈Z