Tangent of Difference

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Corollary to Tangent of Sum

$\map \tan {a - b} = \dfrac {\tan a - \tan b} {1 + \tan a \tan b}$

where $\tan$ is tangent.


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