8sin²x+sinxcosx+cos²x-4·1=0
8sin²x+sinxcosx+cos²x-4(sin²x+cos²x)=0
8sin²x+sinxcosx+cos²x-4sin²x-4cos²x=0
4sin²x+sinxcosx-3cos²x=0 |÷cos²x
4tg²x+tgx-3=0
tgx=t
4t²+t-3=0
D=1-4·4·(-3)=49
t₁=(-1-7)/8=-1 t₂=(-1+7)/8=6/8=3/4=0,75
tgx=-1 tgx=0,75
x=arctg(-1)+πn x=arctg0,75+πk, k∈Z
arctg(-1)=-arctg1
arctg1=π/4
x=-π/4+πn, n∈Z