Cotangent of 195 Degrees

Theorem

$\cot 195 \degrees = \cot \dfrac {13 \pi} {12} = 2 + \sqrt 3$

where $\cot$ denotes cotangent.


Proof

\(\ds \cot 195 \degrees\) \(=\) \(\ds \map \cot {360 \degrees - 165 \degrees}\)
\(\ds \) \(=\) \(\ds -\cot 165 \degrees\) Cotangent of Conjugate Angle
\(\ds \) \(=\) \(\ds 2 + \sqrt 3\) Cotangent of $165 \degrees$

$\blacksquare$


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
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