Trong các khẳng định sau, khẳng định nào sai \(\cos a - \cos b = 2\sin \frac{{a + b}}{2}.\sin \frac{{a - b}}{2}\)

A. \(\cos a + \cos b = 2\cos \frac{{a + b}}{2}.\cos \frac{{a - b}}{2}\)

B. \(\sin a - \sin b = 2\cos \frac{{a + b}}{2}.\sin \frac{{a - b}}{2}\)

C. \(\cos a - \cos b = 2\sin \frac{{a + b}}{2}.\sin \frac{{a - b}}{2}\)

D. \(\sin a + \sin b = 2\sin \frac{{a + b}}{2}.\cos \frac{{a - b}}{2}\)