Cotangent of 30 Degrees

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Theorem

$\cot 30 \degrees = \cot \dfrac \pi 6 = \sqrt 3$

where $\cot$ denotes cotangent.


Proof

\(\ds \cot 30 \degrees\) \(=\) \(\ds \frac {\cos 30 \degrees} {\sin 30 \degrees}\) Cotangent is Cosine divided by Sine
\(\ds \) \(=\) \(\ds \frac {\frac {\sqrt 3} 2} {\frac 1 2}\) Cosine of $30 \degrees$ and Sine of $30 \degrees$
\(\ds \) \(=\) \(\ds \sqrt 3\) multiplying top and bottom by $2$

$\blacksquare$


Sources