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The given expression for \( y \) is:

\[
y = \sqrt{\sec^2(x) + (\tan(x))} + \frac{3 - \tan(3x)}{5x + \cot^3(3x)}
\]

Let's break it down:

1. The first part of the expression involves a square root:
   \[
   \sqrt{\sec^2(x) + \tan(x)}
   \]
   Here, \( \sec^2(x) \) is the square of the secant of \( x \), and \( \tan(x) \) is the tangent of \( x \).

2. The second part is a rational function:
   \[
   \frac{3 - \tan(3x)}{5x + \cot^3(3x)}
   \]
   This includes the tangent of \( 3x \), and the cube of the cotangent of \( 3x \) in the denominator.

If you want further details on how to solve or analyze this equation, feel free to ask!

Would you like me to expand on simplification, differentiation, or any other aspect of this function?

Here are five questions related to this expression:
1. Would you like to simplify the trigonometric expression further?
2. Are you interested in finding the derivative of \( y \) with respect to \( x \)?
3. Should I evaluate this expression for a specific value of \( x \)?
4. Would you like to discuss the behavior of this function as \( x \) approaches specific limits?
5. Do you need assistance with solving for \( x \) in any specific context?

**Tip:** When dealing with trigonometric functions, it's useful to recognize common identities like \( \sec^2(x) = 1 + \tan^2(x) \) to simplify expressions.

Find the value of y for the given trigonometric expression: y = sqrt(sec^2(x) + tan(x)) + (3 - tan(3x)) / (5x + cot^3(3x))

In this problem, we explore a trigonometric expression involving sec^2(x), tan(x), and cot^3(3x). Learn how to simplify and solve for y using key trigonometric identities and formulas, suitable for students in Grades 11-12.

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