Question

Sin5x+sinx=√3*cosx Помогите пожалуйста

Answer 1

Sin5x+(sinx-√3cosx)=0
sin5x+2(1/2*sinx-√3/2*cosx)=0
sin5x+sin(x-π/3)=0
2sin(3x-π/6)cos(2x+π/6)=0
sin(3x-π/6)=0⇒3x-π/6=πn⇒3x=π/6+πn⇒x=π/18+πn/3,n∈Z
cos(2x+π/6)=0⇒2x+π/6=π/2+πn⇒2x=π/3+πn⇒x=π/6+πn/2,n∈Z