Answer
$ \sin x $
Work Step by Step
Given expression is-
$ \frac{\sec x - \cos x}{\tan x} $
( cot and tan are reciprocal)
= $ (\sec x - \cos x )\cot x $
= $ \sec x \cot x - \cos x \cot x $
= $ \frac{1}{\cos x} \frac{\cos x}{\sin x} - \cos x \frac{\cos x}{\sin x} $
( Writing in terms of sin and cos using reciprocal and ratio identities)
= $ \frac{1}{\sin x} - \frac{\cos^{2} x}{\sin x} $
= $ \frac{1 - \cos^{2} x}{\sin x} $
= $ \frac{\sin^{2} x}{\sin x} $
( From first Pythagorean identity, $1 - \cos^{2}x$ = $\sin^{2}x$)
= $ \sin x $
