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 | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac {\sin \theta} {\sin \theta} \frac {\cos \theta} {\cos \theta}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 1\) |
$\blacksquare$