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📅 April 29, 2026 👤 scraface

Apr 29, 2026

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f(x) = \sin^2 x + \cos^2(2x)
We use trigonometric identities to simplify and analyze the expression...
\sin^2 x = rac{1 - \cos 2x}{2}, \quad \cos^2(2x) = rac{1 + \cos 4x}{...
f(x) = rac{1 - \cos 2x}{2} + rac{1 + \cos 4x}{2} = rac{1}{2} - rac...
f(x) = 1 + rac{1}{2}(\cos 4x - \cos 2x)
Now, use the identity for $ \cos 4x - \cos 2x $:
\cos A - \cos B = -2 \sin\left(rac{A+B}{2}
ight)\sin\left(rac{A-B}{2}
Let $ A = 4x $, $ B = 2x $:
\cos 4x - \cos 2x = -2 \sin(3x)\sin(x)

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