已知函数f(x)=2cosxsin(x+π/3)-根号3sin^2x+sinxcosx 当x∈[0,π/4]时,f(x)的值域
问题描述:
已知函数f(x)=2cosxsin(x+π/3)-根号3sin^2x+sinxcosx 当x∈[0,π/4]时,f(x)的值域
答
f(x)=2cosxsin(x+π/3)-√3*(sinx)^2+sinxcosx=2cosx[sinxcos(π/3)+cosxsin(π/3)]-√3*(sinx)^2+sinxcosx=sinxcosx+√3*(cosx)^2-√3*(sinx)^2+sinxcosx=2sinxcosx+√3*[(cosx)^2-(sinx)^2]=sin2x+√3*cos2x=2sin(...