# Cotangent of 45 Degrees

From ProofWiki

## Theorem

- $\cot 45^\circ = \cot \dfrac {\pi} 4 = 1$

where $\cot$ denotes cotangent.

## Proof

\(\displaystyle \) | \(\displaystyle \) | \(\displaystyle \) | \(\displaystyle \cot 45^\circ\) | \(=\) | \(\displaystyle \) | \(\) | \(\displaystyle \) | \(\displaystyle \frac {\cos 45^\circ} {\sin 45^\circ}\) | \(\displaystyle \) | \(\displaystyle \) | Cotangent is Cosine divided by Sine | ||

\(\displaystyle \) | \(\displaystyle \) | \(\displaystyle \) | \(\displaystyle \) | \(=\) | \(\displaystyle \) | \(\) | \(\displaystyle \) | \(\displaystyle \frac{\frac {\sqrt 2} 2} {\frac {\sqrt 2} 2}\) | \(\displaystyle \) | \(\displaystyle \) | Cosine of 45 Degrees and Sine of 45 Degrees | ||

\(\displaystyle \) | \(\displaystyle \) | \(\displaystyle \) | \(\displaystyle \) | \(=\) | \(\displaystyle \) | \(\) | \(\displaystyle \) | \(\displaystyle 1\) | \(\displaystyle \) | \(\displaystyle \) | multiplying top and bottom by $\dfrac {\sqrt 2} 2$ |

$\blacksquare$

## Sources

- Murray R. Spiegel:
*Mathematical Handbook of Formulas and Tables*(1968)... (previous)... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles