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The problem asks to find an expression equivalent to:

\[
1 - 2\sin^2(\theta) + \sin^4(\theta)
\]

We can factorize this expression by recognizing it as a perfect square:

\[
1 - 2\sin^2(\theta) + \sin^4(\theta) = (1 - \sin^2(\theta))^2
\]

Using the Pythagorean identity:

\[
1 - \sin^2(\theta) = \cos^2(\theta)
\]

Thus, the original expression becomes:

\[
(1 - \sin^2(\theta))^2 = \cos^4(\theta)
\]

Therefore, the correct answer is:

\[
\boxed{\cos^4(\theta)}
\]

Would you like more details or have any questions?

Here are five related questions to deepen understanding:
1. What is the Pythagorean identity in trigonometry?
2. How do you factor perfect square trinomials?
3. Can you derive other identities using \(\sin^2(\theta)\) and \(\cos^2(\theta)\)?
4. How would you expand \(\cos^4(\theta)\) if asked to do so?
5. What are some practical applications of trigonometric identities?

**Tip:** Always keep the Pythagorean identities handy as they help simplify trigonometric expressions efficiently.

Which of the following is equivalent to 1 - 2sin^2(θ) + sin^4(θ)?

Find the equivalent expression for 1 - 2sin^2(θ) + sin^4(θ). This problem explores key trigonometric concepts, including the Pythagorean identity and factoring techniques, and is suitable for students in Grades 9-12.

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