Question

sin²x + 6sinxcosx + 8cos²x=0
3tgx – 6ctgx + 7=0

Answer 1

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