若角α为锐角,且sin(a-π/6)=4/5,则cosα=?
问题描述：
若角α为锐角,且sin(a-π/6)=4/5,则cosα=?
答
sin(a-π/6)=4/5
cos(a-π/6)=√[1-sin²(a-π/6)]=√(1-16/25)=3/5
cosα=cos[(α-π/6)+π/6]
=cos(a-π/6)cosπ/6-sin(a-π/6)sinπ/6
=3/5x√3/2-4/5x1/2
=(3√3-4)/10