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Proof: Angle Difference for Sine

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\sin \left(\alpha - \beta \right) = \sin \alpha \cdot \cos \beta - \sin \beta \cdot \cos \alpha

Prerequisites

Proof

\sin \left(\alpha - \beta \right) = \sin \left(\alpha + (-\beta) \right)

Via the Angle Sum for Sine identity:

\sin \left(\alpha - \beta \right) = \sin \alpha \cdot \cos (-\beta) + \sin (-\beta) \cdot \cos \alpha

Via the Negative Angle Identities:

\sin \left(\alpha - \beta \right) = \sin \alpha \cdot \cos \beta - \sin \beta \cdot \cos \alpha

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