π/6＜θ＜π/2
0＜θ-π/6＜π/3
所以 cos(θ-π/6)>0
因为 sin(θ-π/6)=5/13
所以 cos(θ-π/6)=12/13
cosθ=cos[(θ-π/6)+π/6]=cos(θ-π/6)cos(π/6)-sin(θ-π/6)sin(π/6)
=(12√3-5)/26