若3sinx-根3cosx=2根3sin(x-ρ)ρ∈（-π,π）则ρ=_数学解答

若3sinx-根3cosx=2根3sin(x-ρ)ρ∈（-π,π）则ρ=

人气：445 ℃　时间：2020-09-20 04:16:15

解答

3sinx-√3cosx
=2√3(sinx*√3/2-cosx*1/2)
=2√3(sinxcosπ/6-cosxsinπ/6)
=2√3sin(x-π/6)
=2√3sin(x-ρ)
所以ρ=π/6