Question

sinx+cosx,√3sinx+cosx,sinx+√3cosx

几道辅助角公式题~~sinx+cosx=？ sinx-cosx=？ sinx+根号3*cosx=？ sinx-根号3*cosx=？ 根号3*sinx+cosx=？ 根号3*sinx-cosx=？

Answer 1

sinx+cosx =√2(sinxcosπ/4+cosxsinπ/4) =√2sin(x+π/4) sinx-cosx =√2(sinxcosπ/4-cosxsinπ/4) =√2sin(x-π/4) sinx+根号3*cosx =2(sinxcosπ/3+cosxsinπ/3) =2sin(x+π/3) sinx-根号3*cosx =2(sinxcosπ/3-cosxsinπ/3) =2sin(x-π/3) 根号3*sinx+cosx =2(sinxcosπ/6+cosxsinπ/6) =2sin(x+π/6) 根号3*sinx-cosx =2(sinxcosπ/6-cosxsinπ/6) =2sin(x-π/6)