matrix transformation for trig identities

Hi folks,

Given that the following matrix creates an anticlockwise rotation of the x-y plane about the origin through an angle $\displaystyle \theta $:

$\displaystyle \left( \begin{array}{cc}

\cos\theta & -\sin\theta \\

\sin\theta & \cos\theta

\end{array} \right)

$

use this fact to obtain the standard trig identities:

$\displaystyle \sin(\theta + \alpha) = \sin\theta\cos\alpha + cos\theta\sin\alpha

$ and

$\displaystyle \cos(\theta + \alpha) = \cos\theta\cos\alpha - \sin\theta\sin\alpha

$

I can obtain the identities using geometry and I can see how the matrix transformation creates an anticlockwise rotation, but I can't see how to use the matrix trransformation to generate the identities. Can anyone help?