已知∈(0,∏)且cos(a-∏/6)=3/5,求cosa

题目

已知∈(0,∏)且cos(a-∏/6)=3/5,求cosa

答案

a∈(0,π)
cos(a-π/6)=3/5
sin(a-π/6)=4/5
cosa=cos[(a-π/6)+π/6]
=cos(a-π/6)*cosπ/6-sin(a-π/6)*sinπ/6
=3/5*1/2-4/5*√3/2
=3/10-4√3/10