ПОМОГИТЕЕ!!!! ДОКАЖИТЕ ТОЖДЕСТВО

Решите задачу:

$\cos \alpha -\cos(60^\circ- \alpha )-\cos(60^\circ+ \alpha )=\\\\=\cos \alpha -(\cos(60^\circ- \alpha )+\cos(60^\circ+ \alpha ))=\\\\\cos \alpha -2\cos\frac{60^\circ- \alpha +60^\circ+ \alpha }{2}\cos\frac{60^\circ- \alpha -60^\circ- \alpha }{2}=\\\\=\cos \alpha -2\cos60^\circ\cos(- \alpha )=\cos \alpha -2\cos60^\circ\cos\alpha=\\\\\cos \alpha -2\bullet\frac{1}{2}\cos \alpha=\cos \alpha -\cos \alpha =0.$