Cotangent of 105 Degrees
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Theorem
- $\cot 105^\circ = \cot \dfrac {7 \pi} {12} = -\left({2 - \sqrt 3}\right)$
where $\cot$ denotes cotangent.
Proof
| \(\ds \cot 105^\circ\) | \(=\) | \(\ds \cot \left({90^\circ + 15^\circ}\right)\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds - \tan 15^\circ\) | Cotangent of Angle plus Right Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds - \left({2 - \sqrt 3}\right)\) | Tangent of 15 Degrees |
$\blacksquare$
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles