7 tg x – 12ctg x + 8 = 0

Question

7 tg x – 12ctg x + 8 = 0

Answer 1

7tgx - 12ctgx +8 =0

7tgx - 12/tgx +8=0 |*tgx

7tg²x +8 tgx-12 =0 

D=8²+4*7*12=400

t1=-2
t2=6/7

Возвращаемся к замене

tgx=-2
x=-acrtg2 + πn, n ∈ Z
tg x= 6/7
x=arctg(6/7) + πn, n ∈ Z

Answer 2

7tgx+12/tgx+8=0
7tg²x+8tgx-12=0
tgx=a
7a²+8a-12=0
D=64+336=400
a1=(-8-20)/14=-2⇒tgx=-2⇒x=-arctg2+πn
a2=(-8+20)/14=6/7⇒tgx=6/7⇒x=arctg6/7+πn