3π/4<α<π
-5π/6<π/6-α<-7π/12
所以cos(π/6-α)<0
sin²(π/6-α)+cos²(π/6-α)=1
所以cos(π/6-α)=-2√3/3
原式=cos[π/2-(π/2+α)]=cos(π/6-α)=-2√3/3