Question

Хелп плиз
$cos6x+4cos2x textgreater 0$

Answer 1

cos(4x+2x)+4cos2x>0
cos4x*cos2x-sin4x*sin2x+4cos2x>0
cos4x*cos2x-2sin²2x*cos2x+4cos2x>0
cos2x*(cos4x-2sin²2x+4)>0
cos2x*(2cos²2x-1-2+2cos²2x+4)>0
cos2x*(4cos²2x+1)>0
4cos²2x+1>0 при любом х⇒
cos2x>0
-π/2+πk<2x<π/2+πk
-π/4+πk/2<x<π/4+πk/2,k∈z