High School Trigonometry/Sum and Difference Identities for Sine, Cosine and Tangent

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\sin{(u \pm v)} = \sin{u}\cos{v} \pm \cos{u}\sin{v}

\cos{(u \pm v)} = \cos{u}\cos{v} \mp \sin{u}\sin{v}

\tan{(u \pm v)} = \frac{\tan{u} \pm \tan{v}}{1 \mp \tan{u}\tan{v}}