The expression you're dealing with is:

\[
\sqrt{1 - \sin(2x)}
\]

While it's simplified as is, let's break it down:

1. The expression \(\sin(2x)\) refers to the double-angle identity for sine.
2. The square root function is defined for non-negative values. Hence, the expression \(1 - \sin(2x)\) should remain non-negative, which is true if \(\sin(2x) \leq 1\).

If you're looking for specific further steps, transformations, or evaluations, let me know!

Would you like more details or explanations on this?

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Here are five related questions to expand on this concept:
1. What is the double-angle identity for \(\cos(2x)\)?
2. How can \(\sin(2x)\) be expressed in terms of \(\sin(x)\) and \(\cos(x)\)?
3. What is the domain of the function \(\sin(2x)\)?
4. Can we simplify \(\sqrt{1 - \sin(2x)}\) for any specific values of \(x\)?
5. What are the possible values of \(\sin(2x)\) for different ranges of \(x\)?

**Tip**: Always check the domain restrictions of trigonometric functions, especially when dealing with square roots.

Understand how to work with the expression √(1 − sin(2x)) by exploring the double-angle identity for sine and related trigonometric concepts. This explanation includes key trigonometric identities and considerations of domain restrictions for high school students, Grades 10-12.

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