Applying angle addition formulas for subtraction The angle addition formula says that:
$\sin(\phi + \theta) = \sin(\phi) \cdot \cos(\theta) + \cos(\phi) \cdot \sin(\theta)$
Why are the following steps valid?:
$\sin(\phi − \theta) = \sin(\phi) \cdot \cos(−\theta) + \cos(\phi) \cdot \sin(−\theta)= \sin(\phi) \cdot \cos(\theta) − \cos(\phi) \cdot \sin(\theta)$
Thanks.

They're valid because of the following identities:


*

*$\qquad\sin(-\theta) \equiv -\sin(\theta) \qquad\text{since sin is an}$ odd function.

*$\qquad \cos(-\theta) \equiv \cos(\theta) \qquad\text{since cos is an} $ even function.

The $\equiv$ symbol means "is equal to for all (permitted) values of $\ \theta$".
