若函数f(x)=2sin^2x-2根号3sinxsin(X-派\2)能使得不等式|f(X)-m|

问题描述:

若函数f(x)=2sin^2x-2根号3sinxsin(X-派\2)能使得不等式|f(X)-m|
答案是(1,2]

sin(x-π/2)=sin(x+3π/2)=-cosx2sin²x=1-cos2x2sinxcosx =sin2xf(x)=2sin²x-2√3 sinxsin(x-π/2)=1-cos2x+2√3 sinxcosx=1-cos2x+√3sin2x=1+2sin(2x-π/6)不等式|f(X)-m|