📝 Hyperbolic Identities

📖 From Calculus • 7. Applications of the Definite Integral In Geometry, Science, and Engineering • 19 questions available

Practice MCQs for Hyperbolic Identities. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-16

Easy Questions

Medium Questions

Hard Questions

Q1. Which of the following is the correct hyperbolic Pythagorean identity?

🔹 A. \(\cosh^2 x - \sinh^2 x = 1\)

🔹 B. \(\cosh^2 x + \sinh^2 x = 1\)

🔹 C. \(\sinh^2 x - \cosh^2 x = 1\)

🔹 D. \(\cosh^2 x - \sinh^2 x = 0\)

💡 Difficulty: easy | ✅ Correct: A

Q2. Given \(\cosh x = 5\) and \(x>0\), find \(\sinh x\).

🔹 A. \(\;3\sqrt{5}\)

🔹 B. \(\;2\sqrt{5}\)

🔹 C. \(\;5\sqrt{2}\)

🔹 D. \(\;2\sqrt{6}\)

💡 Difficulty: medium | ✅ Correct: D

Q3. Evaluate \(\int \sinh^{2}x\,dx\).

🔹 A. \(\frac{1}{2}(\sinh x\cosh x - x) + C\)

🔹 B. \(\frac{1}{2}(\cosh 2x - x) + C\)

🔹 C. \(\frac{1}{4}\sinh 2x - \frac{x}{2} + C\)

🔹 D. \(\frac{1}{2}(\sinh x\cosh x - x) + C\)

💡 Difficulty: hard | ✅ Correct: D

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