\( \left. \begin{array} { l }{ \frac { \sin ^ { 2 } t } { \cos t } = \sec t - \cos t } \\ { \frac { \sin ^ { 2 } t } { \cos t } = \frac { \square } { \cos t } } \\ { = \square } \\ { = \square } \\ { = \sec t - \cos t } \end{array} \right. \)

Did you know the identity \(\sec t = \frac{1}{\cos t}\) can really help simplify trigonometric equations? Here, you've got \(\frac{\sin^2 t}{\cos t} = \sec t - \cos t\). By substituting \(\sec t\) with \(\frac{1}{\cos t}\), you can eventually see how the sine and cosine functions work intricately together! When working with trigonometric identities, a common mistake is overlooking the Pythagorean identity \(\sin^2 t + \cos^2 t = 1\). Always remember to keep this in mind while simplifying! For example, recognizing \(\sin^2 t = 1 - \cos^2 t\) can be immensely helpful in rewriting functions to find missing pieces in your equation. Happy solving!