cos(α-π/6)=cos(α-π/2+π/3)
=cos(-π/2+α+π/3)
=cos[-(π/2-α-π/3)]
=cos(π/2-α-π/3)
=cos[π/2-(α+π/3)]
=sin(α+π/3)
=√[1-cos² (α+π/3)]
=√[1-(1/5)²]
=(2√6)/5
cos(α-π/6)=cos(α-π/2+π/3)
=cos(-π/2+α+π/3)
=cos[-(π/2-α-π/3)]
=cos(π/2-α-π/3)
=cos[π/2-(α+π/3)]
=sin(α+π/3)
=√[1-cos² (α+π/3)]
=√[1-(1/5)²]
=(2√6)/5