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Home » what happened to rachel maddow last night - Redraw

what happened to rachel maddow last night - Redraw

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 + rac{\sin^2 x + \cos^2 x}{\sin^2 x \cos^2 x} = 5 + rac{1}{\sin^2 x \cos^2 x}

📌 But \(\sin^2 x \cos^2 x = rac{1}{4} \sin^2 2x\), so:

📌 = 5 + rac{4}{\sin^2 2x}

📌 Minimum occurs when \(\sin^2 2x\) is maximized, i.e., \(\sin^2 2x = 1\) when \(x = rac{\pi}{4}\)

📌 Then value is \(5 + 4 = 9\)

📌 Question: Find the range of the function \(f(x) = rac{2\sin x + 3}{\sin x + 2}\) as \(x\) ranges over all real numbers such that \(\sin x

📌 e -2\) (which is always true since \(\sin x \in [-1,1]\)).

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