cos(a+5π/12)cos(a+π/6)+cos(π/12-a)cos(π/3-a）
=sin(π/2-(a+5π/12))cos(a+π/6)+cos(π/12-a)sin(π/2-(π/3-a）)
=sin(π/12-a)cos(a+π/6)+cos(π/12-a)sin(a+π/6)
=sin(π/12-a+a+π/6)
=sin(π/12+π/6)
=sinπ/4
=√2/2