Final answer:
The question pertains to high school level mathematics, requiring the evaluation of an expression involving trigonometric functions, powers, and roots. Step-by-step explanation and example calculations are essential for understanding and simplifying the given complex expression.
Step-by-step explanation:
The question provided involves multiple mathematical concepts, including functions, trigonometry, absolute values, powers, and square roots. The content loaded and complex expressions suggest this is best suited to high school students, likely those studying pre-calculus or calculus. To evaluate the expression, one would need to substitute the given values of x into the expression and simplify, applying trigonometric identities, power rules, and properties of square roots and absolute values where necessary.
The details provided about different equations and their rearrangements give insights into the type of manipulations needed to solve such expressions. The references to squaring and square rooting and trigonometric functions like cosine indicate the mathematical operations required for evaluation. For instance, to evaluate something like the square root of the cosine of x multiplied by the cosine of 200x, you'd need to first find the cosine of x and of 200x, multiply them together, and then take the square root of the product.
Step-by-step explanations are crucial when dealing with compound expressions, especially to avoid making errors when working with minus signs, powers, or trigonometric functions. Example calculations, such as squaring a number and then taking the square root, can help us understand the properties of powers and roots.