3sinx-根号3cosx=2根号3sin（x+α）.α属于（-π,π）,则α的值是

题目

3sinx-根号3cosx=2根号3sin（x+α）.α属于（-π,π）,则α的值是

答案

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