Tangent of Difference/Proof

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
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