Question

Помогите решить систему уравнений

Answer 1

{cos2x=1/2⇒2x=+-π/3+2πk⇒x=+-π/6+πk,k∈z
{sin3x=-1⇒3x=-π/2+2πk⇒x=-π/6+2πk/3

-π≤-π/6+πk≤π
-6≤-1+6k≤6
-5≤6k≤7
-5/6≤k≤7/6
k=0⇒x=-π/6
k=1⇒x=-π/6+π=5π/6

-π≤π/6+πk≤π
-6≤1+6k≤6
-7≤6k≤5
-7/6≤k≤5/6
k=-1⇒x=π/6-π=-5π/6
k=0⇒x=π/6

-π≤-π/6+2πk/3≤π
-6≤-1+4k≤6
-5≤4k≤7
-5/4≤k≤7/4
k=-1⇒x=-π/6-2π/3=-5π/6
k=0⇒x=-π/6
k=1⇒x=-π/6+2π/3=π/2
Общие для 1 и 2:x=-5π/6 и x=-π/6
Ответ 2