cos11pi/12+cos5pi/12

cos11\pi/12+cos5\pi/12=2cos \frac{11\pi/12+5\pi/12}{2}*cos \frac{11\pi/12-5\pi/12}{2}=\\\\=2cos16\pi/24*cos6\pi/24=\\\\=2cos2\pi/3*cos\pi/4=2*(-1/2)*( \sqrt{2}/2)=- \sqrt{2}/2