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

${\displaystyle \sin {(u\pm v)}=\sin {u}\cos {v}\pm \cos {u}\sin {v}}$
${\displaystyle \cos {(u\pm v)}=\cos {u}\cos {v}\mp \sin {u}\sin {v}}$
${\displaystyle \tan {(u\pm v)}={\frac {\tan {u}\pm \tan {v}}{1\mp \tan {u}\tan {v}}}}$