\sec \dfrac{11\pi}{6}

=\sec(2\pi-\dfrac{\pi}{6})

=\sec \dfrac{\pi}{6}

Because the secant function is the reciprocal of the cosine function, we know

\cos \dfrac{\pi}{6}=\dfrac{\sqrt{3} }{2}

\sec \dfrac{\pi}{6} =\dfrac{2\sqrt{3} }{3}

which is also the value of \sec \dfrac{11\pi}{6}