What do you mean by the "definition of a formula"? The identities for the sine and cosine of a sum of angles are found here.
In this link -
Pauls Online Notes : Linear Algebra - Examples of Linear Transformations
When he is talking about 2D rotations, he says -
Now, through a trig formula we can write the equations for w as follows,
I was wondering where a formal definition for this formula can be found. Thanks for any help.