Answer
$\sec\theta$ = $\frac{1}{\sqrt {1-\sin^{2}\theta}}$
Work Step by Step
We are supposed to write $\sec\theta$ in terms of $\sin\theta$ while $\theta$ lies in Quadrant I.
Using ratio identity for $\sec$-
$\sec\theta$ = $\frac{1}{\cos\theta}$
($\cos\theta\ne0$ as $\theta$ lies in quadrant I)
From Pythagorean identity-
$\cos\theta$ may be written as $\sqrt {1-\sin^{2}\theta}$
Therefore-
$\sec\theta$ = $\frac{1}{\sqrt {1-\sin^{2}\theta}}$
