Tangent of Difference/Proof
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Corollary to Tangent of Sum
- $\map \tan {a - b} = \dfrac {\tan a - \tan b} {1 + \tan a \tan b}$
Proof
\(\ds \map \tan {a - b}\) | \(=\) | \(\ds \frac {\tan a + \map \tan {-b} } {1 - \tan a \, \map \tan {-b} }\) | Tangent of Sum | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac {\tan a - \tan b} {1 + \tan a \tan b}\) | Tangent Function is Odd |
$\blacksquare$
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Tangents of sum and difference