Sin²x + 6sinxcosx + 8cos²x=0

3tgx - 6ctgx + 7=0

1) sin²x+6sinxcosx+8cos²x=0 / cos²x≠0

tg²x+6tgx+8=0

tg²x=a

a²+6a+8=0

a1+a2=-6 U a1*a2=8

a1=-4⇒tgx=-4⇒x=-arctg4+πn

a2=-2⇒tgx=-2⇒x=-arctg2+πn

3tgx-6ctgx+7=0

3tgx-6/tgx+7=0

3tg²x+7tgx-6=0 tgx≠0

tgx=a

3a²+7a-6=0

D=49+72=121

a1 = (-7-11) / 6=-3⇒tgx=-3⇒x=-arctg3+πn

a2 = (-7+11) / 6=2/3⇒tgx=2/3⇒x=arctg2/3+πn