Ответ:       - √2/2.

Пошаговое объяснение:

cos(5π/12) -cos(π/12) =>

разность косинусов:

cos a - cos b = -2sin((a-b)/2) *sin((a+b)/2)

cos 5п/12 - cos п/12 =>

********

5π/12-π/12 = 4π/12 = π/3 => (π/3):2 = π/6 .

5π/12+π/12 = 6π/12 =π/2 => (π/2):2 = π/4.

***********

-2sin(п/6)*sin(п/4) = -2*1/2*(√2)/2 = - √2/2.