Sin(2x-п/2)=-1/2 принадлежащие промежутку: (0;3п/2)

Question

Sin(2x-п/2)=-1/2
принадлежащие промежутку:
(0;3п/2)

Answer 1

Sin(2x-π/2)=-1/2
sin(-(π/2-2x)=-1/2
-sin(π/2-2x)=-1/2
sin(π/2-2x)=1/2
cos2x=1/2
2x=π/3+2πn
х=π/6+πn
х∈(0;3π/2)  ⇒
х₁=π/6  x₂=7π/6.