Sine of Difference/Proof 2
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Theorem
- $\map \sin {a - b} = \sin a \cos b - \cos a \sin b$
Proof
| \(\ds \map \cos {90 \degrees + a - b}\) | \(=\) | \(\ds \map \cos {90 \degrees + a} \cos b + \map \sin {90 \degrees + a} \sin b\) | Cosine of Difference | |||||||||||
| \(\ds \leadsto \ \ \) | \(\ds \map \sin {a - b}\) | \(=\) | \(\ds \sin a \cos b - \cos a \sin b\) | Cosine of Angle plus Right Angle, Sine of Angle plus Right Angle |
$\blacksquare$
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: The addition formulae