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.

Hint:
$\cos(\theta)$ is an even function while $\sin(\theta)$ is an odd function.
Hence:
$$\cos(-\theta) = \cos(\theta),$$ 
while
$$\sin(-\theta) = -\sin(\theta).$$
(See this Wikipedia link on Even and odd functions for more information.)
