QuestionSimplify each expression. $$\begin{array}{l} (\tan (t)-\sec (t))(\tan (t)+\sec (t))= \\ (\sec (t)-1)(\sec (t)+1)=\square \\ (1-\sin (t))(1+\sin (t))=\square \end{array}$$

Studdy Solution
Apply the difference of squares identity to the expression $(1 - \sin(t))(1 + \sin(t))$:
$$1^2 - (\sin(t))^2$$
Recall the Pythagorean identity: $1 - \sin^2(t) = \cos^2(t)$.
Thus, the simplified expression is:
$$\boxed{\cos^2(t)}$$