Answer
$ \cos^{2} x $
Work Step by Step
Given expression is-
$ \frac{2 + \tan^{2} x }{\sec^{2} x} - 1 $
= $ \frac{1 + 1 + \tan^{2} x }{\sec^{2} x} - 1 $
= $ \frac{1 + \sec^{2} x }{\sec^{2} x} - 1 $
( From second Pythagorean identity, $1 + \tan^{2} x$ = $\sec^{2} x$)
= $ \frac{1 }{\sec^{2} x} + \frac{ \sec^{2} x }{\sec^{2} x} - 1 $
= $ \cos^{2} x + 1 - 1 $
= $ \cos^{2} x $
