已知sinθ+√3cosθ=2cos(θ-φ),求tanφ.(0
问题描述:
已知sinθ+√3cosθ=2cos(θ-φ),求tanφ.(0
答
sinθ+√3cosθ=2cos(θ-φ)
=>2sin(θ+π/3)=2cos(θ-φ)
=>sin(θ+π/3)=cos(φ-θ)
=> (θ+π/3)+ (φ-θ)=2kπ+π/2
=>φ = 2kπ+π/2-π/3 =2kπ+π/6
又∵ 0