8sin² x + sin x × cos x + cos² x - 4 =0

Question

8sin² x + sin x × cos x + cos² x - 4 =0

Answer 1

8sin²x+sinxcosx+cos²x-4sin²x-4cos²x=0
4sin²x+sinxcosx-3cos²x=0/cos²x
4tg²x+tgx-3=0
tgx=a
4a²+a-3=0
D=1+48=49
a1=(-1-7)/8=-1⇒tgx=-1⇒x=-π/4+πn
a2=(-1+7)/8=3/4⇒tgx=0,75⇒x=arctg0,75+πk,k∈z