Sinx-根号3cosx=6-4m要使其有意义,求m取值范围

题目

Sinx-根号3cosx=6-4m要使其有意义,求m取值范围

答案

sinx-根号3cosx=6-4m
2(sinxcosπ/3-cosxsinπ/3) = 6-4m
2sin(x-π/3) = 6-4m
-2≤2sin(x-π/3)≤2
∴-2≤6-4m≤2
-8≤-4m≤4
-1≤m≤2