# Cotangent of 45 Degrees

## 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 $\dfrac {\sqrt 2} 2$

$\blacksquare$