1+cos 8x =cos 4x найти корни примера

Question

1+cos 8x =cos 4x найти корни примера

Answer 1

1+cos 8x =cos 4x
2cos²4x-cos4x=0
cos4x*(2cos4x-1)=0
cos4x=0⇒4x=π/2+πk⇒x=π/8+πk/4,k∈z
cos4x=1/2⇒4x=+-π/3+2πk⇒x=+-π/12+πk/2,k∈z