Cotangent of Angle plus Right Angle

Theorem

$\map \cot {x + \dfrac \pi 2} = -\tan x$


Proof

\(\ds \map \cot {x + \frac \pi 2}\) \(=\) \(\ds \frac {\map \cos {x + \frac \pi 2} } {\map \sin {x + \frac \pi 2} }\) Cotangent is Cosine divided by Sine
\(\ds \) \(=\) \(\ds \frac {-\sin x} {\cos x}\) Cosine of Angle plus Right Angle and Sine of Angle plus Right Angle
\(\ds \) \(=\) \(\ds -\tan x\) Tangent is Sine divided by Cosine

$\blacksquare$


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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