Tangent of Angle plus Right Angle

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Theorem

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


Proof

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

$\blacksquare$


Also see


Sources