Sin^2x+9sinxcosx+­14cos^2x=0

Question

Sin^2x+9sinxcosx+­14cos^2x=0

Answer 1

Разделим на cos²x
tg²x+9tgx+14=0
tgx=a
a²+9a+14=0
a1+a2=-9 U a1*a2=14
a1=-7⇒tgx=-7⇒x=-arctg7+πk,k∈z
a2=-2⇒tgx=-2⇒x=-arctg2+πk,k∈z