Question

The identities cos(a-b)=cos(a)cos(b)sin(a)sin(b) and sin(a-b)=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).

Answer 1

Sounds like a good justification to me. Oh, did you mean prove them? In that case, using the identities,

cos(a-b) = cos(a + (-b)) = cos(a) cos(-b) - sin(a) sin(-b)
= cos(a)cos(b) + sin(a) sin(b)

sin(a-b) = sin(a + (-b)) = sin(a) cos(-b) + cos(a) sin(-b)
= sin(a) cos(b) - cos(a) sin(b)

Answer 2

Sin2x