解
a是第四象限
∴
sina<0
∵cosa=5/13
∴sina=-√1-(5/13)²=-12/13——sin²a+cos²a=1
∴cos(a+π/3)
=cosacosπ/3-sinasinπ/3
=5/13×1/2+12/13×√3/2
=(5+12√3)/26