Sine of Difference/Proof 1
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Corollary to Sine of Sum
- $\map \sin {a - b} = \sin a \cos b - \cos a \sin b$
Proof
| \(\ds \map \sin {a - b}\) | \(=\) | \(\ds \sin a \map \cos {-b} + \cos a \map \sin {-b}\) | Sine of Sum | |||||||||||
| \(\ds \) | \(=\) | \(\ds \sin a \cos b + \cos a \, \map \sin {-b}\) | Cosine Function is Even | |||||||||||
| \(\ds \) | \(=\) | \(\ds \sin a \cos b - \cos a \sin b\) | Sine Function is Odd |
$\blacksquare$
Sources
- 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 4.5$. The Functions $e^z$, $\cos z$, $\sin z$