Cotangent of 45 Degrees

Theorem

$\cot 45 \degrees = \cot \dfrac \pi 4 = 1$

where $\cot$ denotes cotangent.

$\ds \cot 45 \degrees$

$=$

$\ds \frac {\cos 45 \degrees} {\sin 45 \degrees}$

$\ds $

$=$

$\ds \frac {\frac {\sqrt 2} 2} {\frac {\sqrt 2} 2}$

$\ds $

$=$

$\ds 1$

dividing top and bottom by $\dfrac {\sqrt 2} 2$

$\blacksquare$

1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles
1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): trigonometric function
2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): trigonometric function