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Home » Solution: Recognize it as a difference of cubes: $ (2a)^3 - (3b)^3 = 8a^3 - 27b^3 $. Alternatively, expand directly: - AMAZONAWS

Solution: Recognize it as a difference of cubes: $ (2a)^3 - (3b)^3 = 8a^3 - 27b^3 $. Alternatively, expand directly: - AMAZONAWS

📅 March 11, 2026 👤 scraface
Mar 11, 2026
Solution: Recognize it as a difference of cubes: $ (2a)^3 - (3b)^3 = 8a^3 - 27b^3 $. Alternatively, expand directly:

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📌 Now combine with \( \cos^2(\phi) = \frac{1}{2} \). The only solution satisfying both is \( \phi = -\frac{\pi}{4} \) (since \( \phi = \frac{\pi}{4} \) would give \( \cos^2 = \frac{1}{2} \), but \( \cos\left(\frac{\pi}{2} + \frac{\pi}{4}\right) = \cos\left(\frac{3\pi}{4}\right) = -\frac{1}{\sqrt{2}} \), not zero). However, satisfying \( \cos\left(\frac{\pi}{2} + \phi\right) = 0 \) implies:
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