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89.
Sum of sines
$\sin \alpha + \sin \beta = 2 \cdot \sin\dfrac{\alpha+\beta}{2}\cdot \cos \dfrac{\alpha-\beta}{2}$
90.
Difference of sines
$\sin \alpha - \sin \beta = 2\cdot \sin\dfrac{\alpha - \beta}{2} \cdot \cos \dfrac{\alpha+\beta}{2}$
91.
Sum of cosines
$\cos\alpha + \cos\beta = 2 \cdot \cos \dfrac{\alpha+\beta}{2} \cdot \cos \dfrac{\alpha-\beta}{2}$
92.
Difference of cosines
$\cos\alpha - \cos\beta = -2 \cdot \sin \dfrac{\alpha+\beta}{2} \cdot \sin \dfrac{\alpha-\beta}{2}$
93.
Sum of tangents
$\tan \alpha + \tan \beta = \dfrac{\sin(\alpha+\beta)}{\cos\alpha \cdot \cos \beta}$
94.
Difference of tangents
$\tan \alpha - \tan \beta = \dfrac{\sin(\alpha-\beta)}{\cos\alpha \cdot \cos \beta}$
95.
Sum of cotangents
$\cot \alpha + \cot \beta = \dfrac{\sin(\beta + \alpha)}{\sin\alpha \cdot \sin\beta}$
96.
Difference of cotangents
$\cot \alpha - \cot \beta = \dfrac{\sin(\beta - \alpha)}{\sin\alpha \cdot \sin\beta}$
99.
Product of sines
$\sin\alpha \cdot \sin \beta = \dfrac{1}{2} \left[ \cos(\alpha-\beta) - \cos(\alpha + \beta) \right]$
100.
Product of cosines
$\cos\alpha \cdot \cos \beta = \dfrac{1}{2} \left[ \cos(\alpha-\beta) + \cos(\alpha + \beta) \right]$