Chứng minh rằng: a) \(\cos a - \sin a = \sqrt 2 \cos \left( {a + \frac{\pi }{4} \right)\); b) \(\sin a + \sqrt 3 \cos a = 2\sin \left( {a + \frac{\pi }{3} \right)\).

Chứng minh rằng:

a) \(\cos a - \sin a = \sqrt 2 \cos \left( {a + \frac{\pi }{4}} \right)\);

b) \(\sin a + \sqrt 3 \cos a = 2\sin \left( {a + \frac{\pi }{3}} \right)\).