Product of Tangent and Cotangent

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Theorem

$\tan \theta \cot \theta = 1$


Proof

\(\ds \tan \theta \cot \theta\) \(=\) \(\ds \frac {\sin \theta} {\cos \theta} \cot \theta\) Tangent is Sine divided by Cosine
\(\ds \) \(=\) \(\ds \frac {\sin \theta} {\cos \theta} \frac {\cos \theta} {\sin \theta}\) Cotangent is Cosine divided by Sine
\(\ds \) \(=\) \(\ds \frac {\sin \theta} {\sin \theta} \frac {\cos \theta} {\cos \theta}\)
\(\ds \) \(=\) \(\ds 1\)

$\blacksquare$