Question

Помогите пожалуйста... 

cos2x-cosx=0

Answer 1

cos2x=2cos²x-1

cos2x-cosx=0,   2cos²x-cosx-1=0,

Замена t=cosx, 2t²-t-1=0,  D=1+2*4=9, t₁=(1-3)/4=-1/2, t₂=(1+3)/4=1

cosx=-1/2, x=±(π-arccos1/2)+2πn,  x=±(π-π/3)+2πn, x=±2π/3+2πn, n∈Z

c0sx=1, x=π+2πk, k∈Z