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Home » Kankuro Naruto’s Hidden Talents: The Genius Manipulator You Didn’t Know About! - Coaching Toolbox

Kankuro Naruto’s Hidden Talents: The Genius Manipulator You Didn’t Know About! - Coaching Toolbox

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 But we want **minimum**, not maximum. Can $ f(x) $ be less than 1?

📌 Try $ x = rac{\pi}{4} $: $ \sin^2 x = \left(rac{\sqrt{2}}{2}

📌 ight)^2 = rac{1}{2} $, $ 2x = rac{\pi}{2} $, $ \cos^2(2x) = \cos^2(rac{\pi}{2}) = 0 $, so $ f = 0.5 + 0 = 0.5 $.

📌 But according to formula: $ f\left(rac{\pi}{4}

📌 ight) = 1 - rac{1}{2}(\cos rac{\pi}{2} - \cos \pi) = 1 - rac{1}{2}(0 - (-1)) = 1 - rac{1}{2}(1) = 0.5 $. Correct.

📌 Can it be smaller? Try $ x $ such that $ \sin^2 x $ is small and $ \cos^2(2x) $ is small.

📌 Try $ x = rac

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