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Home » \(b_7 = 21 + 13 = 34\) - DNSFLEX

\(b_7 = 21 + 13 = 34\) - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 f(\sqrt{2}) = \left( \frac{2\sqrt{2}}{2 - 1} \right)^2 = (2\sqrt{2})^2 = 8

📌 Now check derivative or behavior: as $ s \to 1^+ $, $ f(s) \to \infty $. So minimum occurs at $ s = \sqrt{2} $, i.e., $ x = \frac{\pi}{4} $.

📌 \min (\sec x + \csc x)^2 = 8

📌 Question: A science policy analyst is modeling the efficiency of a new energy policy using the expression

📌 Find the minimum value of this expression for $ x \in (0, \frac{\pi}{2}) $.

📌 We expand both terms:

📌 \sin^2 x + \cos^2 x + \sec^2 x + \csc^2 x + 2(\tan x + \cot x)

📌 Use identity $ \sin^2 x + \cos^2 x = 1 $, and:

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