Question

решите тригонометрические уравнения
5tg x-14ctg x+3=0

Answer 1

ctgx=1/tgx
5tgx-14/tgx+3=0
5tg²x+3tgx-14=0,tgx≠0
tgx=a
5a²+3a-14=0
D=9+280=289
a1=(-3-17)/10=-2⇒tgx=-2⇒x=-arctg2+πn,n∈z
a2=(-3+17)/10=1,4⇒tgx=1,4⇒x=arctg1,4+πk,k∈z