Final answer:
The initial problem about tangent and secant functions is incomplete, thus preventing a precise solution. Trigonometric identities and the Pythagorean theorem are relevant to solving trigonometry-related questions.
Step-by-step explanation:
The question provided involves trigonometric identities and algebraic manipulation, specifically using tangent, secant, and the Pythagorean theorem. However, the question appears to be incomplete or contains errors, making it difficult to provide an exact solution without additional clarification. In general, to solve equations involving trigonometric functions like tangent (tan) and secant (sec), we might use trigonometric identities to express one function in terms of the other and then solve for the variable in question. Consistent with this approach, the Pythagorean theorem often comes into play when dealing with right triangles in trigonometry.
For the other mathematical expressions provided, they seem to be unrelated to the initial question, and each represents varied concepts such as exponent rules, right triangle geometry, force equilibrium conditions, and improper fractions alluding to undefined values. As these snippets are provided out of context, they do not form a coherent problem.