若sin(α+π/6)=1/3,则cos(2π/3-2α)的值为

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/19 22:14:59
若sin(α+π/6)=1/3,则cos(2π/3-2α)的值为若sin(α+π/6)=1/3,则cos(2π/3-2α)的值为若sin(α+π/6)=1/3,则cos(2π/3-2α)的值为cos(

若sin(α+π/6)=1/3,则cos(2π/3-2α)的值为
若sin(α+π/6)=1/3,则cos(2π/3-2α)的值为

若sin(α+π/6)=1/3,则cos(2π/3-2α)的值为
cos(2π/3-2α)
=-cos[π-(2π/3-2α)]
=-cos(π/3+2α)
=-cos[2(π/6+α)]
=-{1-2[sin(π/6+α)]^2}
=-(1-2/9)
=-7/9

sin(α+π/6)=cos(π/2-(a+π/6))=cos(π/3-a)=1/3
如令π/3-a=x,则2π/3-2α=2x
cos2x=2cos²x-1=2*1/9-1=-7/9