Question

Помогите решить!
tg^x=3 на отрезке [-5п/2;-п/2]

Answer 1

tg²x=3
tgx=-√3
x=-π/3+πk
-5π/2≤-π/3+πk≤-π/2
-15≤-2+6k≤-3
-13≤6k≤-1
-13/6≤k≤-1/6
k=-2⇒x=-π/3-2π=-7π/3
k=-1⇒x=-π/3-π=-4π/3
tgx=√3
x=π/3+πk,k∈z
-5π/2≤π/3+πk≤-π/2
-15≤2+6k≤-3
-17≤6k≤-5
-17/6≤k≤-5/6
k=-2⇒x=π/3-2π=-5π/3
k=-1⇒x=π/3-π=-2π/3