根号3sinx+cosx=m-1
2(根号3/2sinx+1/2cosx)=m-1
2(sinxcosπ/6+cosxsinπ/6)=m-1
2sin(x+π/6)=m-1
sin(x+π/6)=(m-1)/2
-1≤sin(x+π/6)≤1
-1≤(m-1)/2≤1
-2≤m-1≤2
-1≤m≤3