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You've uploaded an image showing the equation:

\[
y = \sqrt{1 - 4x^2} + 2x \sec^{-1}(2x)
\]

However, you're asking to change the term \(\sec^{-1}(2x)\) to \(\sin^{-1}(2x)\).

After applying that change, the updated equation becomes:

\[
y = \sqrt{1 - 4x^2} + 2x \sin^{-1}(2x)
\]

Would you like to explore this modified equation further? For example, I can help with its differentiation, integration, or provide a graph. Let me know what you'd like to focus on!

Here are some related questions you might find useful:
1. How do you differentiate the modified equation with respect to \(x\)?
2. Can you find the domain and range of the modified equation?
3. How do you simplify \(\sin^{-1}(2x)\) for specific values of \(x\)?
4. What is the behavior of the function as \(x \to \pm \infty\)?
5. How does the graph of the modified function compare to the original?

**Tip:** For inverse trigonometric functions like \(\sin^{-1}(x)\), the domain and range are crucial to ensure the function is well-defined!

Explore the modification of the equation y = √(1 - 4x^2) + 2x sec⁻¹(2x) by replacing the inverse secant function with the inverse sine function. This trigonometry problem is suitable for high school students in Grades 11-12.

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