[tex]\dfrac{13\pi}6\equiv\dfrac\pi6\mod2\pi[/tex] (in other words, they represent the same angle on the unit circle)
So,
[tex]\sec\dfrac{13\pi}6=\sec\dfrac\pi6=\dfrac1{\cos\dfrac\pi6}[/tex]
You have [tex]\cos\dfrac\pi6=\dfrac{\sqrt3}2[/tex], so [tex]\sec\dfrac\pi6=\dfrac{\sqrt3}2[/tex]
