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 are valid because $\sin(-x) = -\sin(x) \forall_{x \in [0, 2\pi]}$ (sinus is an odd function) and $\cos(-x) = \cos(x) \forall_{x \in [0, 2\pi]}$ (cosine is an even function). You can see this by looking at sinus and cosine graphics.
