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Home » \( S = \frac502(1 + 99) = 25 \times 100 = 2500 \). - Veritas Home Health

\( S = \frac502(1 + 99) = 25 \times 100 = 2500 \). - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 f(x) = (\sec x + \cos x)^2 + (\csc x - \sin x)^2

📌 for $ 0 < x < \frac{\pi}{2} $. We aim to find its minimum value.

📌 First, expand both squared terms:

📌 Add the two expressions:

📌 f(x) = \sec^2 x + \cos^2 x + 2 + \csc^2 x + \sin^2 x - 2

📌 f(x) = \sec^2 x + \csc^2 x + (\cos^2 x + \sin^2 x) + 2 - 2 = \sec^2 x + \csc^2 x + 1

📌 Now express in terms of sine and cosine:

📌 f(x) = \frac{1}{\cos^2 x} + \frac{1}{\sin^2 x} + 1 = \frac{\sin^2 x + \cos^2 x}{\sin^2 x \cos^2 x} + 1 = \frac{1}{\sin^2 x \cos^2 x} + 1

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