cos(2a+π/3)=2cos²(a+π/6)-1=7/25a为锐角,则：2a+π/3∈(π/3,π/2)∴sin(2a+π/3)=24/25sin(2a+π/12)=sin[(2a+π/3)-π/4]=sin(2a+π/3)cosπ/4-cos(2a+π/3)sinπ/4=(17根号2)/50