Answer
$$-\frac{1}{\sqrt{1 - sin^2 \space t}}$$
Work Step by Step
$$sec \space t$$
Using: $sec \space t = \frac{1}{cos \space t}$:
$$\frac{1}{cos \space t}$$
Using: $sin^2\space t + cos^2\space t= 1 $
$cos^2 \space t = 1 - sin^2\space t$
$cos \space t = \pm \sqrt{1- sin^2 \space t}$
Notice: For "t" in Quadrant II, cos t is always negative, thus:
$cos \space t = -\sqrt {1 - sin^2 \space t}$
$$\frac{1}{-\sqrt{1 - sin^2 \space t}} = -\frac{1}{\sqrt{1 - sin^2 \space t}}$$
