Question

2tgx-5ctgx=3
Прошу помогите

Answer 1

2tgx-5/tgx=3
2tg²x-3tgx-5=0,tgx≠0
tgx=a
2a²-3a-5=0
D=9+40=49
a1=(3-7)/4=-1⇒tgx=-1⇒x=-π/4+πn,n∈z
a2=(3+7)/4=2,5⇒tgx=2,5⇒x=artg2,5+πk,k∈z