2sin²x+5sinxcosx+5cos²x=1;

Question

2sin²x+5sinxcosx+5cos²x=1;

Answer 1

2sin²x+5sinxcosx+5cos²x-sin²x-cos²x=0/cos²x
tg²x+5tgx+4=0
tgx=a
a²+5a+4=0
a1+a2=-5 U a1*a2=4
a1=-4⇒tgx=-4⇒x=-arctg4+πn,n∈z
a2=-1⇒tgx=-1⇒x=-π/4+πk,k∈z