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

Question

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

Answer 1

2α－2π/3与2α－π/6差了90度,cos(2α－π/6)=-sin（2α－2π/3）=-2sin（α－π/3）cos（α－π/3）
由α为锐角,sin(α－π/3)=﹣3/5,cos(α－π/3)=4/5,所以cos(2α－π/6)的值为24/25