已知函数f(x)=2sin²x+√3 sin2x-1若方程在f(x-π/6)+4sinx+1=a在x∈[π/6,π/2]_数学解答

已知函数f(x)=2sin²x+√3 sin2x-1
若方程在f(x-π/6)+4sinx+1=a在x∈[π/6,π/2]上有解,求实数a的取值范围

人气：159 ℃　时间：2019-12-08 03:37:51

解答

f(x)=2sin^x+根号3sin2x-1=-(1-2sin^2x)+根号3sin2x=-cos2x+根号3sin2x=2sin(2x-π/6)所以f(x-π/6)=2sin(2x-π/3-π/6)=2sin(2x-π/2)=-2cos2x所以f(x-π/6)+4sinx+1=-2cos2x+4sinx+1=-2(1-sin^2x)+4sinx+1=2sin^2x...