Trig!
posted by Elle .
The identities cos(ab)=cos(a)cos(b)sin(a)sin(b) and sin(ab)=sin(a)cos(b)cos(a)sin(b) are occasionally useful. Justify them. One method is to use rotation matricies. Another method is to use the established identities for cos(a+b) and sin (a+b).

Sounds like a good justification to me. Oh, did you mean prove them? In that case, using the identities,
cos(ab) = cos(a + (b)) = cos(a) cos(b)  sin(a) sin(b)
= cos(a)cos(b) + sin(a) sin(b)
sin(ab) = sin(a + (b)) = sin(a) cos(b) + cos(a) sin(b)
= sin(a) cos(b)  cos(a) sin(b) 
Sin2x