已知α为锐角,且cos(α+π/6)=5/13,则cosα=

已知α为锐角,且cos(α+π/6)=5/13,则cosα=
已知α为锐角,且cos(α+π/6)=5/13,则cosα=

已知α为锐角,且cos(α+π/6)=5/13,则cosα=
展开即可：
cos(α+π/6)=（√3/2）cosα-（1/2）sinα=5/13
sin(α+π/6)=（1/2）cosα+（√3/2）sinα=12/13;
二元一次方程组,就简单了

∵α为锐∴α+π/6∈(π/6,2π/)
∵cos(α+π/6)=5/13,
∴sin(α+π/6)=√(1-25/169)=12/13
cosα=cos[(α+π/6)-π/6]
=cos[(α+π/6)-π/6]
=cos(α+π/6)cosπ/6+sin(α+π/6)sinπ/6
=5/13*√3/2+12/13*1/2
=(5√3+12)/26