Tangent of Difference

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

• 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Formulae $(18)$
• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: $5.36$
• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $2$: Functions, Limits and Continuity: The Elementary Functions: $4$
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): compound angle formulae (in trigonometry)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Appendix $12$: Trigonometric formulae: Addition formulae
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Appendix $14$: Trigonometric formulae: Addition formulae