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The value of \( F(\pi) \) is \( 10 \).

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Here are 5 related questions for further practice:

1. How does the cosecant function behave for different angles?
2. What are the key identities involving cotangent and cosecant?
3. How would the expression change if \( x \) were replaced by \( \frac{\pi}{2} \)?
4. How can the result of \( F(\pi) \) be verified graphically or numerically?
5. How does the complexity of trigonometric expressions affect their simplification?

**Tip**: When dealing with multiple trigonometric functions in a single expression, try simplifying parts individually before combining them.

Se tiene la siguiente expresión: F(x) = (5 * csc(x/6) + 6 * sqrt(3) * ctg(x/3) + 3 * sqrt(2) * cos(x/4) + ctg(x/4)) / ((1/sqrt(2)) * csc^3(x/4)). Calcula el valor de F(π).

Solve for F(π) using trigonometric identities like cosecant, cotangent, and cosine in the given expression. This problem covers core trigonometry concepts and is suitable for students in Grades 11-12.

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