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\binom122 = \frac12 \times 112 = 66 - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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ight) = \sin\left(rac{\pi}{2}
ight) = 1 $, so product = $ -1 $.
Thus $ \sin 3x \sin x = -1 $ is achievable (e.g., $ x = rac{3\pi}{2}...
Wait â we want to **minimize** $ f(x) = 1 - \sin 3x \sin x $, so we...
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] $.
g'(u) = 6u - 16u^3 = 2u(3 - 8u^2)

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