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Home » Das Volumen \( V \) eines rechteckigen Pools wird durch die Formel gegeben: - Groen Casting

Das Volumen \( V \) eines rechteckigen Pools wird durch die Formel gegeben: - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \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:

📌 + (1 + \tan^2 x) + (1 + \cot^2 x) + 2(\tan x + \cot x) = 3 + \tan^2 x + \cot^2 x + 2(\tan x + \cot x)

📌 Let $ t = \tan x + \cot x $. Then:

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