Let's work through the equation step by step:

You are given:

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

### Step 1: Simplify the expression inside the parentheses
We know that:

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

So, we can rewrite the equation as:

\[
\sec^2 \theta \cdot \cos^2 \theta = 1
\]

### Step 2: Use the identity for secant
Recall that:

\[
\sec^2 \theta = \frac{1}{\cos^2 \theta}
\]

Substituting this into the equation, we get:

\[
\frac{1}{\cos^2 \theta} \cdot \cos^2 \theta = 1
\]

### Step 3: Simplify the expression
Since \(\frac{1}{\cos^2 \theta} \cdot \cos^2 \theta = 1\), the equation simplifies to:

\[
1 = 1
\]

### Conclusion:
This is a true statement, meaning the original equation is **identically true** for all values of \(\theta\) where \(\cos \theta \neq 0\) (i.e., \(\theta \neq \frac{\pi}{2} + n\pi\), where \(n\) is an integer).

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Would you like more details or have any questions about this solution? 

Here are some related questions to explore:

1. How can I prove other trigonometric identities using algebraic manipulation?
2. What is the relationship between secant and cosine functions?
3. How do you determine when a trigonometric identity is true for all values of \(\theta\)?
4. How do you solve equations involving secant and sine functions?
5. What are some other common trigonometric identities I should know?

**Tip**: Always remember to simplify trigonometric expressions using known identities (like \( \sec^2 \theta = 1 + \tan^2 \theta \) or \( \sin^2 \theta + \cos^2 \theta = 1 \)) to make solving easier.

Explore the step-by-step solution to the identity sec²(θ)(1 - sin²(θ)) = 1, demonstrating key trigonometric concepts and identities. This problem is relevant for high school students studying trigonometry.

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