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Home » Thus, the smallest such $ n $ is $ \boxed1 $. - Silent Sales Machine

Thus, the smallest such $ n $ is $ \boxed1 $. - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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$ \sin^2 x = 1 \Rightarrow x = rac{\pi}{2} + k\pi $. At $ x = rac{\p...
ight) = 1 + 1 = 2 $.
But earlier algebra:
f(x) = 1 - rac{1}{2}(\cos 2x - \cos 4x)
Let $ x = 0 $: $ \sin^2 0 = 0 $, $ \cos^2 0 = 1 $, $ f(0) = 1 $. Formu...
$ x = rac{\pi}{2} $: $ \cos 2x = \cos \pi = -1 $, $ \cos 4x = \cos 2\...
But earlier we said $ f(x) = 1 - rac{1}{2}(\cos 2x - \cos 4x) $. When...
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(...

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