Дано: 5sin(13π/12)cos(13π/12)

sin(13π/12) = sin(π - π/12) = sin(π)cos(π/12) - cos(π)sin(π/12) = 0cos(π/12) - (-1)sin(π/12) = sin(π/12) = 1/2

cos(13π/12) = cos(π - π/12) = cos(π)cos(π/12) + sin(π)sin(π/12) = -1cos(π/12) - 0sin(π/12) = -cos(π/12) = -√3/2

Теперь подставим значения sin(13π/12) и cos(13π/12) в выражение:

5 (1/2) (-√3/2) = -5√3 / 4

Ответ: -5√3 / 4