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Home » For a square with side $ s $, the diagonal is $ s\sqrt2 $. Therefore: - Midis

For a square with side $ s $, the diagonal is $ s\sqrt2 $. Therefore: - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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\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...
Multiply numerator and denominator by $\sqrt{3} + 1$:
= \frac{(\sqrt{3} + 1)^2}{(\sqrt{3} - 1)(\sqrt{3} + 1)} = \frac{3 + 2\...
\boxed{2 + \sqrt{3}}

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