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📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Let $ u = \sin x \in [-1, 1] $. Then:

📌 \sin 3x \sin x = (3u - 4u^3)u = 3u^2 - 4u^4

📌 Define $ g(u) = 3u^2 - 4u^4 $, $ u \in [-1, 1] $.

📌 g'(u) = 6u - 16u^3 = 2u(3 - 8u^2)

📌 Set $ g'(u) = 0 $: $ u = 0 $ or $ 3 - 8u^2 = 0 \Rightarrow u^2 = rac{3}{8} \Rightarrow u = \pm \sqrt{rac{3}{8}} = \pm rac{\sqrt{6}}{4} $

📌 Evaluate $ g(u) $:

📌 At $ u = 0 $: $ g = 0 $

📌 At $ u = \pm rac{\sqrt{6}}{4} $:

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