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Home » \(27 = 3^3\) - iBuildNew

\(27 = 3^3\) - iBuildNew

📅 April 29, 2026 👤 scraface

Apr 29, 2026

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A_{\text{new}} = \frac{\sqrt{3}}{4} \cdot 12^2 = \frac{\sqrt{3}}{4} \c...
The increase in area is:
\Delta A = 36\sqrt{3} - 54
\boxed{36\sqrt{3} - 54}
Question: Compute $\tan 75^\circ$ using angle addition identities.
Solution: Using the identity:
\tan(a + b) = \frac{\tan a + \tan b}{1 - \tan a \tan b}
Let $a = 45^\circ$, $b = 30^\circ$, so:
\tan 75^\circ = \tan(45^\circ + 30^\circ) = \frac{\tan 45^\circ + \tan...
= \frac{1 + \frac{1}{\sqrt{3}}}{1 - 1 \cdot \frac{1}{\sqrt{3}}} = \fra...

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