Establish the identity. \[ (\sec \theta+\tan \theta)(\sec \theta-\boldsymbol{\operatorname { t a n }} \theta)=1 \] Multiply and write the left side expression as the difference of two squares.

To establish the identity, let's start with the left-hand side of the equation: \[ (\sec \theta + \tan \theta)(\sec \theta - \tan \theta) \] We can recognize this as a difference of squares formula, which states that \( (a + b)(a - b) = a^2 - b^2 \). Here, \( a = \sec \theta \) and \( b = \tan \theta \). Using the difference of squares, we have: \[ = \sec^2 \theta - \tan^2 \theta \] Now, we can use the Pythagorean identity \( \sec^2 \theta - \tan^2 \theta = 1 \). This is derived from the Pythagorean identities: \[ \sec^2 \theta = 1 + \tan^2 \theta \] Thus, substituting into our expression gives us: \[ \sec^2 \theta - \tan^2 \theta = (1 + \tan^2 \theta) - \tan^2 \theta = 1 \] Therefore, we've shown that: \[ (\sec \theta + \tan \theta)(\sec \theta - \tan \theta) = 1 \] And the identity is established!