Cotangent of Angle plus Full Angle

Theorem

$\cot \left({x + 2 \pi}\right) = \cot x$


Proof

\(\ds \cot \left({x + 2 \pi}\right)\) \(=\) \(\ds \frac {\cos \left({x + 2 \pi}\right)} {\sin \left({x + 2 \pi}\right)}\) Cotangent is Cosine divided by Sine
\(\ds \) \(=\) \(\ds \frac {\cos x} {\sin x}\) Cosine of Angle plus Full Angle and Sine of Angle plus Full Angle
\(\ds \) \(=\) \(\ds \cot x\) Cotangent is Cosine divided by Sine

$\blacksquare$


Also see


Sources

  • 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Functions of Angles in All Quadrants in terms of those in Quadrant I
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