Answer
$ \cos\theta$
Work Step by Step
Given expression is-
$\sec\theta - \tan\theta\sin\theta$
= $\frac{1}{\cos\theta} - \frac{\sin\theta}{\cos\theta}\times\sin\theta$
= $\frac{1}{\cos\theta} - \frac{\sin^{2}\theta}{\cos\theta}$
=$ \frac{1 - \sin^{2}\theta}{\cos\theta} $
= $\frac{\cos^{2}\theta}{\cos\theta}$
( From first Pythagorean identity, $ (1 - \sin^{2}\theta)$ can be written as $\cos^{2}\theta$)
= $ \cos\theta$
