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Angle Sum and Difference Identities

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Sine of Difference of Angles

$\sin(\alpha - \beta) = \sin(\alpha)\cos(\beta) - \cos(\alpha)\sin(\beta)$

Cosine of Difference of Angles

$\cos(\alpha - \beta) = \cos(\alpha)\cos(\beta) + \sin(\alpha)\sin(\beta)$

Sine of Sum of Angles

$\sin(\alpha + \beta) = \sin(\alpha)\cos(\beta) + \cos(\alpha)\sin(\beta)$

Cosine of Sum of Angles

$\cos(\alpha + \beta) = \cos(\alpha)\cos(\beta) - \sin(\alpha)\sin(\beta)$

Tangent of Difference of Angles

$\tan(\alpha - \beta) = \frac{\tan(\alpha) - \tan(\beta)}{1 + \tan(\alpha)\tan(\beta)}$

Cotangent of Sum of Angles

$\cot(\alpha + \beta) = \frac{\cot(\alpha)\cot(\beta) - 1}{\cot(\beta) + \cot(\alpha)}$

Tangent of Sum of Angles

$\tan(\alpha + \beta) = \frac{\tan(\alpha) + \tan(\beta)}{1 - \tan(\alpha)\tan(\beta)}$

Cotangent of Difference of Angles

$\cot(\alpha - \beta) = \frac{\cot(\alpha)\cot(\beta) + 1}{\cot(\beta) - \cot(\alpha)}$

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