cos ( π/2 + α) + tg (α + 3 π) = cos(π/2)cos(α) - sin(π/2)sin(α) + sin(α)/(cos(α))

Так как cos(π/2) = 0, sin(π/2) = 1.

cos( π/2 + α) + tg (α + 3 π) = 0cos(α) - 1sin(α) + sin(α)/(cos(α)) = -sin(α) + sin(α)/(cos(α)) = sin(α)(1 - 1/cos(α))

Теперь найдем cos(α) и sin(α):

cos( π/2 + α) = cos(π/2)cos(α) - sin(π/2)sin(α) = 0cos(α) - 1sin(α) = -sin(α)
cos(α) = -sin(α)

sin( α + 3π) = sin(α)cos(3π) + cos(α)sin(3π) = sin(α)(-1) + (-sin(α))0 = -sin(α)

Теперь подставляем найденные значения:

sin(α)(1 - 1/(-sin(α))) = sin(α)(1 + 1/sin(α)) = sin(α) + 1 = 1 (так как sin(α) = 1)

Ответ: 1.