Question

2sin (5П/6-2x)+1= cosП/2

Answer 1

2sin(5π/6-2x)+1=cosπ/2
2sin(5π/6-2x)+1=0
2sin(5π/6-2x)=-1
sin(5π/6-2x)=-1/2
5π/6-2x=(-1)^{n+1}*π/6+πn, n∈Z
-2x=(-1)^{n+1}*π/6-5π/6+πn, n∈Z
x=(-1)^{n+2)*π/12+5π/12-πn/2, n∈Z