Cotangent of Angle plus Three Right Angles

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Theorem

$\map \cot {x + \dfrac {3 \pi} 2} = -\tan x$


Proof

\(\ds \map \cot {x + \frac {3 \pi} 2}\) \(=\) \(\ds \frac {\map \cos {x + \frac {3 \pi} 2} } {\map \sin {x + \frac {3 \pi} 2} }\) 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

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