If SiNx radical 3 times cosx = 2m-3, then the value range of M is the same

If SiNx radical 3 times cosx = 2m-3, then the value range of M is the same

2m-3=sinx-√3cosx
=2sin(x-π/6)
Because sin (x - π / 6) belongs to [- 1,1]
Therefore, 2m-3 belongs to [- 2,2]
That is: - 2 ≤ 2m-3 ≤ 2
1 / 2 ≤ m ≤ 5 / 2