角A是锐角,cos(A+派/6)=4/5,cosA=?

题目

角A是锐角,cos(A+派/6)=4/5,cosA=?

答案

cos(A+派/6)=4/5,sin(A+π/6)=3/5(因为角A是锐角,4/5>0,所以A+派/6也是锐角)
cosA=cos(A+π/6-π/6)
=cos(A+π/6)cosπ/6+sin(A+π/6)sinπ/6
=(4/5)*(√3/2)+(3/5)*(1/2)
=(4√3+3)/10