Trig Angle Sum/Difference Identities
Table of Contents
For arbitrary angles \(\small a\) and \(\small b\), the following are true:
$$ \sin(a + b) = \sin(a) \cos(b) + \cos(a) \sin(b) $$ $$ \sin(a - b) = \sin(a) \cos(b) - \cos(a) \sin(b) $$
$$ \cos(a + b) = \cos(a) \cos(b) - \sin(a) \sin(b) $$ $$ \cos(a - b) = \cos(a) \cos(b) + \sin(a) \sin(b) $$
$$ \tan(a + b) = \frac{\tan(a) + \tan(b)}{1 - \tan(a) \tan(b)} $$ $$ \tan(a - b) = \frac{\tan(a) - \tan(b)}{1 + \tan(a) \tan(b)} $$