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Home » Factor out 9 from \( x \)-terms: - ClickBalance

Factor out 9 from \( x \)-terms: - ClickBalance

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 ight) = 1 $, so product = $ -1 $.

📌 Thus $ \sin 3x \sin x = -1 $ is achievable (e.g., $ x = rac{3\pi}{2} $). But we want **maximum** of $ \sin 3x \sin x $, not minimum.

📌 Wait â we want to **minimize** $ f(x) = 1 - \sin 3x \sin x $, so we want the **maximum** of $ \sin 3x \sin x $.

📌 So we seek $ \max(\sin 3x \sin x) $. Use identity:

📌 \sin 3x = 3\sin x - 4\sin^3 x

📌 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] $.

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