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Home » You Won’t Believe What Happens When You Use Hoopa – It’s Mind-Blowing! - ToelettAPP

You Won’t Believe What Happens When You Use Hoopa – It’s Mind-Blowing! - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Let $ A = 4x $, $ B = 2x $:

📌 \cos 4x - \cos 2x = -2 \sin(3x)\sin(x)

📌 f(x) = 1 + rac{1}{2}(-2 \sin 3x \sin x) = 1 - \sin 3x \sin x

📌 We now seek the minimum value of $ f(x) = 1 - \sin 3x \sin x $. Since $ -1 \leq \sin 3x \sin x \leq 1 $, the maximum of $ \sin 3x \sin x $ is 1, so the minimum of $ f(x) $ is:

📌 We verify this value is attainable. Suppose $ \sin 3x = 1 $ and $ \sin x = 1 $. Then $ x = rac{\pi}{2} + 2\pi n $. Check $ \sin 3x = \sin\left(rac{3\pi}{2}

📌 ight) = -1

📌 e 1 $. Not simultaneous. Try to find $ x $ such that $ \sin 3x \sin x = 1 $. This requires both $ |\sin 3x| = 1 $ and $ |\sin x| = 1 $, and same sign. But suppose $ \sin x = 1 \Rightarrow x = rac{\pi}{2} $, then $ \sin 3x = \sin\left(rac{3\pi}{2}

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