22.4. а) cos (π/10) − cos (π/20); б) cos (11π/12) + cos (3π/4); в) cos (π/5) − cos (π/11); г) cos (3π/8) + cos (5π/4).

Применяем формулы суммы и разности косинусов.

а) \(\cos\frac{\pi}{10}-\cos\frac{\pi}{20}=-2\sin\frac{3\pi}{40}\sin\frac{\pi}{40}\).

б) \(\cos\frac{11\pi}{12}+\cos\frac{3\pi}{4}=2\cos\frac{5\pi}{6}\cos\frac{\pi}{12}=-\frac{3\sqrt{2}+\sqrt{6}}{4}\).

в) \(\cos\frac{\pi}{5}-\cos\frac{\pi}{11}=-2\sin\frac{8\pi}{55}\sin\frac{3\pi}{55}\).

г) \(\cos\frac{3\pi}{8}+\cos\frac{5\pi}{4}=2\cos\frac{13\pi}{16}\cos\frac{7\pi}{16}\).