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We are asked to simplify the following expression:

\[
\text{j: } \sec^4 \theta - 2 \sec^2 \theta \tan^2 \theta + \tan^4 \theta
\]

### Step-by-Step Simplification:

1. **Recognize identities**:
   - Recall the identity: 
     \[
     \sec^2 \theta = 1 + \tan^2 \theta
     \]

2. **Expand terms**:
   Let's try to rewrite this in terms of \(\sec^2 \theta\) and \(\tan^2 \theta\).

   We can factor this expression as a perfect square:
   \[
   \sec^4 \theta - 2 \sec^2 \theta \tan^2 \theta + \tan^4 \theta = (\sec^2 \theta - \tan^2 \theta)^2
   \]

3. **Use the identity**:
   Using the identity \(\sec^2 \theta = 1 + \tan^2 \theta\), substitute into the factored expression:
   \[
   (\sec^2 \theta - \tan^2 \theta)^2 = (1 + \tan^2 \theta - \tan^2 \theta)^2 = 1^2 = 1
   \]

### Final Answer:
\[
\boxed{1}
\]

Would you like further clarification or additional steps? Here are some related questions you may explore:

1. How does the identity \(\sec^2 \theta = 1 + \tan^2 \theta\) help in trigonometric simplifications?
2. Can the original expression be solved using any other method?
3. What is the geometric interpretation of the identity \(\sec^2 \theta - \tan^2 \theta = 1\)?
4. How does this simplification apply in integral calculus?
5. How can this identity be useful in solving trigonometric equations?

**Tip:** Always look for trigonometric identities when simplifying complex expressions!

Simplify the expression: sec^4 θ - 2 sec^2 θ tan^2 θ + tan^4 θ

Learn how to simplify the trigonometric expression sec^4 θ - 2 sec^2 θ tan^2 θ + tan^4 θ using trigonometric identities. This solution covers the secant and tangent functions, suitable for students in Grades 11-12.

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