Cotangent of Angle plus Straight Angle

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Theorem

$\map \cot {x + \pi} = \cot x$


Proof

\(\displaystyle \map \cot {x + \pi}\) \(=\) \(\displaystyle \frac {\map \cos {x + \pi} } {\map \sin {x + \pi} }\) Cotangent is Cosine divided by Sine
\(\displaystyle \) \(=\) \(\displaystyle \frac {-\cos x} {-\sin x}\) Cosine of Angle plus Straight Angle and Sine of Angle plus Straight Angle
\(\displaystyle \) \(=\) \(\displaystyle \cot x\) Cotangent is Cosine divided by Sine

$\blacksquare$


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