Hyperbolic Tangent of Sum/Corollary
< Hyperbolic Tangent of Sum(Redirected from Hyperbolic Tangent of Difference)
Jump to navigation
Jump to search
Corollary to Hyperbolic Tangent of Sum
- $\map \tanh {a - b} = \dfrac {\tanh a - \tanh b} {1 - \tanh a \tanh b}$
where $\tanh$ denotes the hyperbolic tangent.
Proof
| \(\ds \map \tanh {a - b}\) | \(=\) | \(\ds \frac {\tanh a + \map \tanh {-b} } {1 + \tanh a \, \map \tanh {-b} }\) | Hyperbolic Tangent of Sum | |||||||||||
| \(\ds \) | \(=\) | \(\ds \frac {\tanh a - \tanh b} {1 - \tanh a \tanh b}\) | Hyperbolic Tangent Function is Odd |
$\blacksquare$
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 8$: Hyperbolic Functions: $8.22$: Addition Formulas
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $2$: Functions, Limits and Continuity: The Elementary Functions: $5$