Question

Sinxsin3x=1/2 помогите решить!

Answer 1

1/2[сos(x-3x)-cos(x+3x)]=1/2
cos2x-cos4x=1
cos2x-2cos²2x+1=1
cos2x-2cos²2x=0
cos2x(1-2cos2x)=0
cos2x=0⇒2x=π/2+πn⇒x=π/4+πn/2
cos2x=1/2⇒2x=+-π/3+2πn⇒x=+-π/6+πn