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Home » Stop Guessing: The Shocking Truth on How to Crush Mafia! - High Altitude Science

Stop Guessing: The Shocking Truth on How to Crush Mafia! - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 + \sin 2x + rac{4}{\sin^2 2x}

📌 Let \(t = \sin 2x\), \(0 < t \leq 1\) (since \(x \in (0, \pi/2)\Rightarrow 2x \in (0, \pi)\), and \(t = 1\) at \(x = \pi/4\))

📌 Define \(f(t) = 1 + t + rac{4}{t^2}\), \(0 < t \leq 1\)

📌 Derivative: \(f'(t) = 1 - rac{8}{t^3}\)

📌 Set to zero: \(1 = rac{8}{t^3} \Rightarrow t^3 = 8 \Rightarrow t = 2\), not in domain. So maximum occurs at endpoint \(t = 1\)

📌 Then \(f(1) = 1 + 1 + 4 = 6\)

📌 As \(t o 0^+\), \(f(t) o \infty\), but wait â is \(t\) bounded below? Yes, but \(rac{4}{t^2} o \infty\), so function has no maximum?

📌 But in domain \(0 < x < \pi/2\), \(\sin 2x = 0\) is not attained, but approaches 0, so \(rac{4}{\sin^2 2x} o \infty\), so expression tends to infinity?

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