Question

Помогите решить
cos2x-cosx+1=0, [-п;п]

Answer 1

cos²x-sin²x-cosx+1=0
cos²x-(1-cos²x)-cosx+1=0
cos²x-1+cos²x-cosx+1=0
2cos²x-cosx=0
cosx(2cosx-1)=0
cosx=0 и cosx=1/2
x=π/2+- πn и x=π/3 +- πn