化简f(x)=2sin(x+30°)-2cosx

来源：学生作业帮助网编辑：作业帮时间：2024/05/10 20:11:24

化简f(x)=2sin(x+30°)-2cosx
化简f(x)=2sin(x+30°)-2cosx

化简f(x)=2sin(x+30°)-2cosx
f (x)=2sin(x+30°)-2cosx
=2sinxcos30°+2cosxsin30°-2cosx
=√3sinx-cosx
=2(√3/2sinx-1/2cosx)
=2(cos30°sinx-sin30°cosx)
=2sin(x-30°)

原式=2sinxcos30°+2cosxsin30°-2cosx
=根号3sinx-cosx
=-cos(x+π/3)