2cos²x = 8cos2x - sin2x

2cos²x=8(cos²x-sin²x)-2sinxcosx
2cos²x=8cos²x-8sin²x-2sinxcosx
8sin²x+2sinxcosx-6cos²x=0
8tg²x+2tgx-6=0, tgx=t
8t²+2t-6=0
t₁=-1,t₂=3/4
tgx=-1, x=-π/4+πn
tgx=3/4, x=arctg3/4+πk