Question

在教辅助角公式：要使sinA-根号3 cosA=（4m-6）/（4-m）有意义,求m取值范围?

Answer 1

sinA-根号3 cosA=（4m-6）/（4-m）

1/2sinA-√3/2cosA=(2m-3)(4-m)

sin(A-60°)=(2m-3)/(4-m)

-1≤sin(A-60°)≤1

-1≤(2m-3)/(4-m)≤1

(1) (2m-3)/(4-m)+1≥0

(m+1)/(m-4)≤0 -1≤m≤4

(2)(2m-3)/(4-m)-1≤0

(3m-7)/(m-4)≥0

m≥4 或m≤7/3

综合 -1≤m≤7/3