设α为锐角,若cos(α+π/6)=4/5,则sin(2α+π/3)的值为?

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 16:25:02
设α为锐角,若cos(α+π/6)=4/5,则sin(2α+π/3)的值为?

设α为锐角,若cos(α+π/6)=4/5,则sin(2α+π/3)的值为?
设α为锐角,若cos(α+π/6)=4/5,则sin(2α+π/3)的值为?

设α为锐角,若cos(α+π/6)=4/5,则sin(2α+π/3)的值为?
∵cos(α+π/6)=4/5
α是锐角
∴π/6 < α+π/6 < 2π/3
∴sin(α+π/6)=3/5
sin(2α+π/3)=sin[2(α+π/6)]
=2sin(α+π/6)cos(α+π/6)
=2*3/5*4/5
=24/25